Learn how to build a stock investment portfolio and what to expect from stock market investing. | Daniel Andersen | Skillshare

Learn how to build a stock investment portfolio and what to expect from stock market investing.

Daniel Andersen

Learn how to build a stock investment portfolio and what to expect from stock market investing.

Daniel Andersen

Play Speed
  • 0.5x
  • 1x (Normal)
  • 1.25x
  • 1.5x
  • 2x
19 Lessons (2h 26m)
    • 1. Overview

      1:17
    • 2. Who is this course suitable for

      0:48
    • 3. How to load up Solver on MS Excel and Google Sheets

      1:23
    • 4. Risk and return

      9:43
    • 5. Portfolio with minimum variance

      21:01
    • 6. Optimal portfolio of stocks and bank deposit

      13:32
    • 7. Multiple assets portfolio part 1

      18:48
    • 8. Multiple assets portfolio part 2

      8:16
    • 9. Volatility and time horizon

      8:16
    • 10. Capital Asset Pricing Model

      3:11
    • 11. Capital Market Line

      7:13
    • 12. Deconstructing risks

      4:55
    • 13. Security Market Line

      4:39
    • 14. Beta

      4:04
    • 15. Alpha

      10:31
    • 16. Diversification through global portfolio

      11:28
    • 17. Conclusion

      1:16
    • 18. Tests

      2:40
    • 19. Tests and Solutions

      13:20
  • --
  • Beginner level
  • Intermediate level
  • Advanced level
  • All levels
  • Beg/Int level
  • Int/Adv level

Community Generated

The level is determined by a majority opinion of students who have reviewed this class. The teacher's recommendation is shown until at least 5 student responses are collected.

159

Students

--

Projects

About This Class

-This course will go through the basic theory and principles of how to construct a stock investment portfolio and about portfolio and risk management.

-Learn how to calculate the expected return and risk from an investment.

-Specifically, this course will teach you about constructing a minimum variance stock portfolio, based on modern portfolio theory, constructing an optimal portfolio of stocks and risk free asset and constructing a portfolio of multiple assets.

-This is not a precise prediction model, but to set what you can expect of your portfolio. So it's one of the tools you can use to construct a portfolio, but it shouldn’t be your only tool.

Meet Your Teacher

Hello, I'm Daniel.

Currently I am a higher executive officer at NAV or Norwegian Labour and Welfare Administration, where my colleagues and myself administer around a third of the national budget through difference benefits payouts. My main task is to be a case officer for NAV’s clients, by doing their case assessments and writing case resolutions such as approving or denying cases. I have been working in this position for about two years.

Prior to NAV, I have worked 7 years in bank and insurance sectors, such as DNB and Storebrand. I was a case officer in pension and insurance department.

As educational background, I have a Bachelor degree from Oslo community college and Master's degree in finance and economics from Norwegian School of Economics.

... See full profile

Class Ratings

Expectations Met?
  • Exceeded!
    0%
  • Yes
    0%
  • Somewhat
    0%
  • Not really
    0%
Reviews Archive

In October 2018, we updated our review system to improve the way we collect feedback. Below are the reviews written before that update.

Your creative journey starts here.

  • Unlimited access to every class
  • Supportive online creative community
  • Learn offline with Skillshare’s app

Why Join Skillshare?

Take award-winning Skillshare Original Classes

Each class has short lessons, hands-on projects

Your membership supports Skillshare teachers

Learn From Anywhere

Take classes on the go with the Skillshare app. Stream or download to watch on the plane, the subway, or wherever you learn best.

phone

Transcripts

1. Overview: In this course we will learn about portfolio, analysis mainly about portfolio model, risk and return, how to construct a minimum variance portfolio. How to allocate your capital between multiple assets. I will explain about volatility and time horizon, capital asset pricing, model and exercises for you to practice on. In addition, to the powerpoint presentation, I will also be using a spreadsheet for in the presentation, You can either use Microsoft excel or Google sheet and you Should have sold were installed for for no model. The portfolio analysis off this course is best on the world off the economist Harry Markowitz, who introduced the modern portfolio Terry in 1952. That theory assumed that investors are risk averse. Even shoes are less risky. Investments if the expected return on the same and the risk and return threat off are built differently by difference investors, depending on their risk aversion, this is measured by where is understand activation. This is not the press. I prediction modern, but to set what you can expect up your portfolio. So it's one of the tools you can use to construct a portfolio, but it shouldn't be your only tool 2. Who is this course suitable for: who is this course suitable for and who it needs not suitable for. Let's start with Who is this course is not suitable for If you are expecting a strategy to gain high return from investment in a short amount of time, then this course is not for you. This caused office principles of how to construct a portfolio, missed idea, risk and return threat off and how to analyze that portfolio. Presidents Net gives a range of what you can expect from the California in a long run. This course is suitable for those who want to start investing in the stock market or knows that want to have more control off their financial investment. Finance students or experience will find this course helpful in their study or refreshing their competence in finance. 3. How to load up Solver on MS Excel and Google Sheets: Hi. In this video I will show you how to install in the air in Seoul Number for Microsoft Excel You go to fire options Add in Go Take off the box Silver Erin Okay, now go to data and the sort of a Foshan show me here for Google Sheets You go here add ons get add ons Search for the word solver This one click free She was your Google account click allow and the ad on should be here there. 4. Risk and return: risk and return. They expect that the return is con created by summing up the return off each scenario off investment more deprived by their probability off giving that return. You can also use historical return to conflate the expected return. But the actual return might very greatly from historical return, when there are changes in the systematic risks like new products. New competition The risk of an asset is expressed by weary INTs. Wherein isn't a measurement on the spread from the expected return, the higher the spread very scary East. The investment wherein is con created from the spread from the expected return. Those breast can cancelling out each other and give variants value off. Zero. So to avoid librarians to be zero, we convert the data to a square form before Khan creating variance. Standard deviation is the square with optimum arians. This is to convert the data back to the same skin as it was originally started with. Standard duration is most common amongst traders and on a list to use this concrete, the expected return and where Ian's here is an investment with three possible outcomes, the probability off each outcome is 50% for scenario one 20% fascinated two and 30% for Scenario three no return up. Each scenario is 10% in scenario, 15% in snare two and 20% in scenario three. The expected return is calculated by multiplying the probability off each scenario is their respective return and some of the results. This gives the expected return off 20% where it is complicated by adding together the square well off the spread between the return off each scenario and the expected return and multiplied by the probability off each scenario, it's better to see the calculation. In practice, you take the return off ish scenario. Miners expected return rise by two to get the square value will deprive by the probability off that scenario and use some of the results. This gives the wariness off 0.31 Standard deviation is the square root off the variance. This gives standard deviation off 5.57%. Assuming the returns follow on nor amount distribution. The wrestled tells us that 68% off the time the return will spread one standard deviation from the expected return, either positive or negative. So 68% off the time. The return wouldn't be between 18% and 6% 95% of the time. Two standard deviations 99% of the time. Three. Standout deviation. So 95% of the time, the return will be between 23% and 1%. 99% of the time. The return will be between 29% and minus 5%. Now, let's do the previous congregation with a stock. Here we have closing prices of Apple on the first of June issue from 2000 and 8 to 2000 and 18. The later is from Yahoo Finance. Since we don't know what happens, future scenarios are or the probability off the scenarios and their returns. We've been used the historical stock price to compute the expected return. This is complicated by finding the average yearly return to concrete the return for any given year. You take the price off that year over the price off previous year, minus one, we drank the former down to concrete the rest of our data. Now we take the average off our returns. This gives us on arithmetic return off 31.9%. The number of income in handy later when we are congregating variants and co variance for an investor, the arithmetic mean isn't accurate as the expected return because it doesn't consider the compounding effect. Compounding effect is when you reinvest the return from the previous year's Are. So you're saying arithmetic mean as expected, Return doesn't account for gaining back the lost You might have heart from the pit previous years. Trust me. Even be using the CLO metric means toe find the more adequate yearly return to find the kill metric mean we at the number one to each year's return. This is so we can get the interest factor from each year Return For example, in 2000 and nine, you had 3% return. This gives 1.3 interest factor. We move the pride, the result like this. We raised the result by one well with him because we want to find the yearly return from a 10 years compounded return minus one took on with the data back to what we started with Miss give Geometric mean off 28.3%. Excel also has a form formula to complete geometric. I mean the input French Is this French? Also minus one. This Get Gilman took me and up 28.3%. Same result. Do you remember how to congregate? Variance. We take the return on each year subject by the magnetic expected return all in a square form tow Avoid turning variance to zero. Since our data set is quite large, me used the excellent formula for this are rather set is constant a sample from a population. So we'll be using this formula Variants point It's stands for sample. This keeps various off zero point sit on my six standard deviation is the square root off Mirren's It's the standard deviation is 31%. So in this video we have gone to how to conquer it the expected return variance and start out deviation And we happened to how to use the historical return as expected Return Remember that the actual return can very greatly from the history computer and how to concrete the geo metric means. On the next video, we will be adding stocks and construct a portfolio 5. Portfolio with minimum variance: expected return off a two assets portfolio. The expected return open to asset for for no is the weighted expected return from the assets in the portfolio. Put for no risk or Aaron's is conflated. By using this formula, we need to find coherence between the assets before became conflict. The variance guerra is the measurements off the dependency between the return octo assets. It is computed by taking the difference between assets number ones return and it's expected to return and multiply it with difference between as its number two's return. And it's expected. Return the Why the results With the Koran data set minus one eat the that is a sample off our population. Suarez is in absolute term, which means it measures how much toe assets change in tandem with one mother. Correlation is a relative measurements off the dependency, which means it tells how strong toe assets change in tandem with one another, less confident the poor for low risk and return on a special. Here we have the yearly coursing prices up Amazon from July 2008th 2000 and 18 us before we conquered the geometric mean using these interest factors and charismatic mean using the yearly returns you find there were Ian's and the star, not deviation for how to concrete these values. You can check out the previous video to find the core variance. We can start by setting up a covert reels. Metrics. Coherence is computed by taking the difference between assets number ones return and it's expected, return and multiply it with the difference between assets and what was return. And it's expected. Return divine the results with the total numbers off sample minus one. See sound Data set is quite large. We've been used fresh it formula to oppose, even used this recent from happen and I'm a song and the expected return data Korans is defined us using the arithmetic mean so we'll be using arithmetic mean us the expected return. We set up the court, whereas metrics, - we've been used in multi function for this and most more surprise two sets up area. The first area in the former must be in a row form. Why in the second array must be in a column form. Since our data set is in the column form, we need to convert it to a row form to use us. The first area even used transports function for that. So we transposed these columns. Why sub subjecting out the expected return? Multiply it be the same matters again, this time with abusing transports by substrate ing the expected return divide with the total number of data set 10 minus one. When you are working with metrics former, you need to press control shift enter instead off enter When confirming the formula hunter on shift enter there. From the coherence metrics, you can see the coherence between Apple and Amazon US. Minus zero 0.0 Same in seven. A stock school Reverence between the center is the burials. You can confirm it here. Apple's various zero points. No. 096 The same must be co created earlier. That's concrete. Part four knows return. We're starts by having 30% in Apple and 70% in Amazon for simplicity and consistency. Even used the arithmetic. I mean, as the expected return enterprise went with the expected return and some of the result. This gives the return off 37%. When you have 38% of your capital in Apple and 70% in Amazon for weapons, we will use this former We take the with all apple rising by two. More than five is wearing off admin, plus the with off Amazon Rise my to with the prime with the awareness of Amazon plus two the private the with up apple well, the private the with off Amazon and monitor private. The coherence mystery, and Apple and Amazon escaped the remnants off 0.49 and started deviation off 22%. You can also use excellent former to co create these two results for the port for no return . We want to multiply these variables, these barriers and some of the result. You can use a multi function for that. The first area must be in Rome for so this Paris second area must be in column form, possibly been reducing these two bedrooms. And as you can see, you get the same result for where ins. We basically want to more deprived than wear rings and co Reverend Smith ICS with each asset with in the portfolio, and then they want to multiply again with each asset spent in the portfolio so we can start by using and mold and and multi again and the first every must be in a row for but the wedded in a column form. So we will use transpose return. Supposed to come birth. The data set from quorum to a role and sick ordinary is a column form. We can use this where in school, whereas metrics Baidu's and then will deprive that again missed the with offish assets in the portfolio. And since this is the area formula, you confirm the form run by pressing control. Shift, enter. And, as you can see, you get the same result minimal. Where is buffalo? This is a performer on that has the optimal weight of asset which minimize the portfolios. Variants mess on the performer where INS formula. We find the well off asset number one that keeps the minimum variance. We do this by taking the derivative off. The former are with the respect off asset number one. Instead, it equal to zero. We solve the equation for asset number one escaped in the former for the optimum waiter, a set number one that gives minimum variance. Let's conquered at this using except we even used this former happen will be our asset number one. We start by taking the variants are Asset number two. In this case, Amazon miners coherence between apple and Amazon do y that by where ins happen plus bearings off Amazon minus two more The prime by the coherence between apple and Amazon. This cape about 48% in happen and about 52% in Amazon. On this scale, 36% return and 21 person found that deviation. You can also use the spreadsheets, solver function, tow conflict, the minimum variance portfolio. To do that, we can start by ending a role here for summing up the assets with Click on somewhere is under the data pair after you have installed it is here on how to Islam Somber. Shake one off the introduction videos off this course. Let's first turn the allocation back to 30. 70. Now we've been used sorrow to find the minimum variance portfolio somewhere set the objective variants us minimal by changing these two variables, then we set a constraint. And when these cells must be equal to 100% that means one. Okay, some there. Okay. As you can see, you get the same. Result us what be completed manually earlier. Let's add more companies in the portfolio. Here we have Google, Microsoft and Burke shy. We complete the returns. The Willian's and dis turned out deviations the same way I read it on Apple and Amazon. Check the previous video on how to complete these values to be able to complete the portfolios variants we need. The Coburn insists between these assets. Koreans is computed by taking the spread from the expected return, often asset, and multiply it with the spread off, not the asset. We will expand our very coherence metrics. Here again, we will be using the Immelt and transpose former US. We select the area are reason to be shown me. We transposed this year Really turns column. Took on work them from columns to rose minus the expected returns to find a split when the private the same columns minus the expected return divided by the number off sample in this case 10 and minus one because it's a sample of a bigger population. So it's been lying and control shift enter because this is them. Every formula. Now we concrete the way Reince are. Poor boy Delawareans formula is for two assets for more than two assets. We need to Conklin it every combination off coherence and variance between each stock and some of the wrestles. This is quite tedious, so we will use spreadsheets. Former auto help us. But first we set up random ways of investment Inish stock in this case, one off the total investment in its stock there , 20% investment in issue stock. We will be multiplying. This is the where Ian's co variance matrix adjusted for the with each stock, so a multi twice and transpose the wit well, surprise with the wear in school weapons metrics and with the private the waste of each stock control shift enter. This gives the weapons up 0.1 and start not division off 11%. We still haven't contradicted the portfolio's return. As mentioned earlier. You can use Excel formula to simplify the calculation. So Immelt the first already wouldn't be days role. Second area wouldn't be this column enter. This gives for for your return off 24%. Now let's find the minimum Marion's Portfolio B venue Sorber function for this so data. So what? And the minimum I this cell, the variance. By changing these values and keeping the totem made toe 100%. So it's one. Okay, so Miss Game. This locations Apple 10%. I must on 20% 26% in Google, 19% in Microsoft, 33% in work shy. And these give a portfolio return off 20%. Where is upset up 101 and start on division off. 10. If you don't want to have more than 25% off your total capital invested in one stock, you can set constraints in silver. You do this by going to get our Sorber, and these range of settles less or equal to 25%. It's OK. So okay, this gift 25% off your total capital invested in Google, Microsoft and work shy wide event percent in Apple and 14% in Amazon. And the escapes return up 21% per year. And where it's off, syrup went 011 stone activation off 11%. In this video, we learned about how to construct, Aware and school various metrics, how toe Consulate Portfolio's return and where it ends and how the concrete a minimum. Wearing his portfolio in the next video we will include the option toe also advocate a proportion off the total capital interbank deposit and also include investment in author kind of asset in this case in a bond fund. 6. Optimal portfolio of stocks and bank deposit: off the mountain location. Multiple assets. In this video, we will look into a location between a performer off stocks and the risk free investment in this case, a bank deposit. We windrow capital our location line, a line that shows the return from difference combinations off stock performed no and the bank the posted Rian first find the combination off stocks that maximizes the shops. Preshow charts ratio is the risk adjusted excess return. The expected return on the portfolio is calculated by this formula when the why is the West off the escape or for low and one minus y is the wet up bank deposit. How much a person should invest in wine depends on that person's crystal Russian, and there is awash in court. Isn't the higher the value of the proportion invested in their escape or for no decreases? I want to go too much into this topic, but usually Risk Aversion Corp isn't isn't higher than five, but some economists have are good that it can go hired and fired when we know in The Discoloration Corp isn't and the investors expected return, we can calculate how much the investor shown are located in the capital into the risky portfolio. We add more rows in our spread Shit shot. Wish you risk aversion core percent. Why, that is the wet in the stock portfolio and one minus y. That is the wet in the bank deposit also called him for the risk free return. A one year certificate of deposit is the moment around 2.6%. We will use it to represent the risk free rate. Let's first find the combination of stocks that maximizes the shops from Asia. Sharpe ratio is there is just that return. Basically the return that existed the risk free rate when you take on one more unit of risk . So you take the return off the portfolio minus the risk spirit divided by start an innovation off the perform you. This gives 1.71 Sharpe ratio For the poor formula that we constructed earlier. We will be using Sarver function off the spread Shit, Mr where we can find the maximum matter off this cell by changing the well off these cells . So data summer set this cell to maximum by changing these cells me at a cost rent and sit. These settle to be equal to 100%. That means one. Okay, some. Okay, This gives 22% in Apple, 24% in Amazon, 41% in Google, 6% in Microsoft and work try. And this gives the Sharpe ratio of 1.90 return of 26% and started out deviation off 200%. We can also set a constraint so that you don't invest more than 25% off your total capital into one company. So it's all over, and these cells less or equal to 25%. Okay, so okay, this gives 25% in Amazon and in Google, 21% in Apple, 16% in Microsoft course, 15% in back Brookshire. And this gives Sharpe ratio of 1.89 return up 25% in the stone of duration of 20%. Now we can draw the capital on location line online. That shows the return from reference combinations off stock portfolio and the bank deposit . So in search even used a scepter shark, this one right click, select data and stuck. But funny or any time expended can be understand that division off the portfolio. The Y value can be the return off just for 40. Okay. Okay. There. Be a good Also include the return and stone on innovation off the bank deposit. So right, click. Select data. Ah, the expenditures. Since it's discreet, their standard deviation can be zero. And the wire would be the risk free rate 2.6%. Okay. Okay, there we will make a line between these two points. So insert ships this one there. This is the competent location line. It shows the extra return from the risk free rate. The more risk you take. Let's add labels on our shark in a move the line temporarily and decide and element religion. But, um, there be it and back the line. And also ah, data labels there. The proportion off the total capital that should be invested in this portfolio depends on the investor risk. Aversion Corp isn't it will use these formula and the risk aversion Corvis and up to so expected to turn off the portfolio minus there is created the right by toe with the prime. I risk operation conversant well of pride by the wearing off the portfolio and set the blankets. Also, he said, a constraint so that the proportion doesn't go over 100% but there with the risk and return or term person Istana division and 25% expected return. This keeps us 100% on the carpet on that can be that will be located to their escape or for your and zero to bank deposit to a better illustrate the concept off missile version less instead of using expected return off. Our stock portfolio is that we will use the expected return off the S and P 500. Here we have the expected return off the S and P 500 understand out deviation. So it's very subversion, Corvis and still us too. The escapes when you take the expected return in this case the S and P 500 minus the risk free rate 2.6% Divide by to on the prime by the risk aversion conversant and with a private guide, the wearing off the S and P 500 set them blankets So this gives 69% in the S and P 500 and 31% in the bank deposit. We will use this former to concrete the return and a standard deviation off the optimal. But for you So with the return, you take the wet in the S and P 500 when the pride by the expected return plus the weight in the bank deposit more the prime mind the risk free rich. This gave the expected return off 7.4% and start on division or just take the weight off the S and P 500 multiplied by the starting situation on the S and P five. This gives turnout division off 11%. So foreign investor without risk aversion off to and who believes that the returns from the S and P 500 is the representative for For Sheri Dillon, this location is the most optimal tradeoff between risk and return. You can change the wearables around to see how it affects the optimal allocation. For example, if it increased the risk aversion, coffee isn't too three. This increases the bank deposit proportion and the portfolio return moves to what there is free, right? Also it they risk abortion corpus and stays on change. But there is free rate rises quite something to 4%. This also increase the bank deposit proportion. We can also see these changes in the real life when the risk free rate, like the 10 years treasure bills, rise to AH, certain live in the stock market falls right after one of the reasons might be due to the investors need to reallocate the cover time to achieve a new optimum portfolio. On this video, we have learned how to construct a stock portfolio that maximizes Sharpe ratio how through there are capital allocation line and construct an optimal portfolio consisting off stocks and bank deposit. In the next video, we will learn how to include other kind of asset into the optimum portfolio in this case, a bond fund. 7. Multiple assets portfolio part 1: now we will include another asset in our portfolio for this widow, even construct a portfolio consisting off stocks, bonds and the risk free asset munis didn't be using bank deposit as our risk free asset. We really draw on efficient frontier, a craft that shows for follows off stocks and bonds that give I just expected return for a given star, not deviation even used the part foreign off that maximizes charts ratio. Then we will find the proportion off our capital that should be invested in that port. Follow the rest can stay in the bank. Let's include order kind of asset in our portfolio. In this example, we've been included the Fidelity in New Markets Income, which is bond fund that holds mostly emerging market bonds be used. The historical return us the expected return. The fund gives us the return off 7.3% and start our division off 8%. Let's first up. There are rare in school where ins metric, so it also includes the bond fund. So the market, the area and Imo transpose the return minus expected returns. The prime by the same area minus the expected return divided by the number that asset minus one I controlled shift Enter there. We will use this to concrete the coherence business in the stock portfolio and the fun. We do this by multiplying the wet off a stock in the portfolio, Mr. As co parents with the farm and some of the results. So a mult the transport's these area and will deprive is this five Rules and Control shift and third and there with the coherence between the stock for for no and the Bond fund calculate that we can construct on efficient frontier a craft their shows risk and return from combinations off stock portfolio and the bond fund. We will set up a set off combinations between the stock portfolio and the bond fund. - Now we concrete their risk and return off ish combination for how to concrete the risk and return off a portfolio. You can check out one the previous videos. Basically, we will use this former us so you take the wet on the stock portfolio. Will the prime by the return on the stock for for new plus the weight of the born multiplied by the return on the bond there where wins. So you take the with off the stock. But for new rice, my to will deprive. By the way, rinse off the stock portfolio, plus the with but the bond fund rise by two. Well, the prime, By the way, rinse off the bond fund plus two when the prive ide the wet off the stock for for no multiplied by the with off the bond fund and multiplied by the core variance between the Stockport for no and the bond fund there and stormed out deviation. Now we put this data into a craft, so insert scattered shark select data and the X value can be in there. Sunda deviations the Wiranto's indeed, um, returns. Okay, Okay, there. This it is called the efficient frontier. Is the combinations off the access with their correspondent expected return and start out deviation This just an line here there and be with at the risk free rate. I should like data and zero there is clear it is 2.6% and even make a line from the risk free rate and the point where the line Hankins the Efficient Frontier, beat the combination between stock portfolio and bond fun that has the highest Sharpe ratio there. We will also use armor function to find the combination off the risky portfolio and the bond fund that has the highest Sharpe ratio. So there remove the sell down a bit. Stop portfolio. So we set up the with and being just oh, the these cells there. It's back up. We conclude the risk and return the same way immediate. Earlier you sing this to a former us so we can just could be the former up from here and change the way livers the width there. Aaron's Meta Skopje from here shake the wearable for the wet star, not duration is the square root of Barron's for the shop. Racial even. Just use this formula here. Return from the portfolio This one minus the risk re ridge 2.6% divide by starting out innovation off the for for no. So it this one change it to general there and maybe you sort of want to maximize the shop. Misha, by changing the way in the stock portfolio. So data somewhere set objective this cinnamon to mix. It's even better. By changing this cell clustering, the sum must be equal to 100%. Okay, so okay, this gives 71% in this stock portfolio, 29% in the bond fun, and this gives the return up 20% and start a division of 9% and Sharpe ratio 1.9 to 5. So this on location gives the highest well off sharp regime. I just exceeds return. Four ish unit operates. You're taking reinsert the result into our graph. So select data head stock experiment can be this stone on division. Why better? It's the return okay there and then decide at minimum religion there. This changed the cargo, so it's more visible there. So as you can see, the part formula is where the competent on location life tankan's the efficient frontier. So it's here at Liberals Day. The liberals, right? We only keep two labels on the efficient frontier. So now we can collect the proportion off the total capital we want to allocate in this stock and bond portfolio and the rest into the bank deposit. Assuming the risk awash in core essence is still too. You've been copy these roles, we will use niece formula. So we set a constraint so that so that the proportion doesn't exceed 100% on may. Take the expected return on the portfolio minus the risk free rich divide by tool When the Pride by the Reservation Corp isn't and what a fine, by the way, rinse off the stock and born for follow set blankets there. This gives 100% into the stock and born but for now and zero in the bank deposit. 8. Multiple assets portfolio part 2: as in the previous video, to better show the concept off risk aversion even used the S and P 500 instead off our stock portfolio combined with the bond fun. So even combined the holding in the S and P 500 with the holding in the bond phone and concrete How much should be invested in the pot for you And how much for me in there? It's very asset. So we first find a combination off S and P 500 the bond fun that gives the highest Sharpe ratio. It's just copy this, Rose. Yeah, and put in the data before we can concrete the variance. We need to concrete the co variance between the S and P 500 the bond fun. So a multi transpose, uh, minus the expected return when the prime by same area then divide by nine controlled, shipped in there. This is the core members within S and P 500 the born phone. Now we can cooperate. The wear rings even just copied the former from here and all the change this to this and this to this you can check the previous videos on if you don't remember how to co create the where it's and this give the stone occupational 15% and a concrete sharper issue. So you take the expected return minus. There is clear it divided by startup division off the portfolio. And they use solar word to Mexico minder shop raise you. So, uh, next changing this and keeping this to 100% there, so they don't have 20% in the S and P 500 and it a present in the bone phone. If you want to maximize the shop ratio now, we can co create how much will be invested in this perform you and how much room stay in the bank deposit. So you just take the expected return here minus the risk free rate divide by two provider risk aversion. Corporate since to on the prime. By the way, parents on the port for new said Rankin's here there also set a constraint so that the poor potion doesn't exceed 100%. This gives I stayed in 100% to me in the stock and bond and Sea Rovers and in the bank deposit escaping the return off Stop duration. You can increase the risk aversion. Corvis in five missed the risk. Aversion Cove isn't US five, given the present more in the bank deposit 18% in the bank, deposit and editores and in this stock and born in the S and P five minute it and born phone portfolio. It's give 6.10 expected return in 6% stone on deviation. In this video, we have include a bond fund in our portfolio. We construct an efficient from care and found the combination between stock portfolio and the bond phone that gives highest Sharpe ratio. And then we found an optimal location between the stock and born for for noise and the bank deposit. We found that 100% of our competition should be in the stock and bond part for, you know, and to better illustrate the risk aversion and optimal location, we change our stock portfolio, toe the S and P 500 and combine that with the bond fund and foul on optimal on occasion between the portfolio and the bank deposit. In the next video, we believe on the Terri off relativity and the time horizon 9. Volatility and time horizon: one on the assumption or pricing model is that prices make a random walk. The past movements in prices don't predict the future price movements. This makes the movements in where it is purported to movements in time. For example, tow conflict annual wearing You motor private told her where ins with one over the total number of gs. And as we know, the standard deviation is the square goes off the variance To find the and Ron started activation Mona Private locum stand activation with the square of the one over the total number of years, like in the show formula. So mathematically startup duration increases less The longer the horizon. To illustrate this, even used the risk and return off the S and P 500. The s and P 500 has about NY prison Yeary arithmetic return and 15% year lease. Don't not deviation even calculate what the return will be in 10 years and what the standard duration will be in 10 years even used these area here. This coral will be the year to concrete the return for each year. You just take one plus the year in return. The brink it Yeah, rise by the year minus one and just drag down the formula. So in year one, you get in the return of 9%. You re invest the return that get you 19% total return in year two and so forth. Remember, this is just a matematica only Alvarez schmitter and confirmation You might get a higher return than 9% on one year and lower than 9% on the other. The numbers don't account for inflation. We inserted data into a graph. So in Cirque schedule, right click select data and the expert who can be the year the wire and lose would be the return there. As you can see, the return keep rising the longer you hold the investment. Now let's Coakley it the variance and the star not deviation. So there. So you just take the wearing ends off the S and P 500 Want pride by the number of years and so not deviation is the square root off Marin's. So we just put the data into a graph in Cirque schedule. Citic Data and expert who is the year y values stone at division. Okay, okay. As you can see, the stone on innovation doesn't rise. As Sharp asked, Every tune, the longer you hold. The investment has brought both data into one shark. So in search schedule on Cilic data and ex Mero is the year why? Well, it's the return and then so that data and year not New Asian. See that the longer you home the investment, you will have more to lose. But the volatility rises slower to sum up. Stop pricing model assumes a random walk in pricing. The past movements don't predict the future movements, thus making the movements in where ins proportion toe the movements in time. Two years, wherein is equal to one year where ins multiplied by to and still not deviation is the square root off where Ian's so two years down, activation is equal toe. One year stone activation multiplied by the square root up to that's making the star not division, move slower the wrong the type pricing, as mentioned in one of the previous video stone activation, is what most analyst use for measuring rece 10. Capital Asset Pricing Model: in this part. Off the video, we will look into capital asset price motor. It is central shortness as captain, because over what capital market line is, we will look into how the total risk off a stock investment is considered off. Dropping the security market line calculating better and are far away lives off. A company kept him is used to determine the require return, often investment. The formula consists off risk Cleary. It expected. Return off the market portfolio and better off the investment there. Some assumptions we need to have in mind. Most important are one. Investors are rational and risk averse, expected return and where it's are used to determine an investor investing decision. This assumes that investors require risk premium to take on additional risk. Toe financial markets are competitive. And if isn't, it assumes that most investors are well informed about the financial market making That's its price efficient three frictionless market. Without transaction costs and taxes, these assumptions might sound unrealistic, but they were necessary to be able to create the cap and motor they have been near. Studies where the assumptions are less strict in the wrestling still support the motors men implications. You can use this modern as one of your auto financial terms and miss your own judgment to better explain. Kept em imagines that you want to invest in the company pepper, but you don't know even expected. Every return off 31.9% a year is worth the risk up. 31% were agility. Using kept em calculation. You compared the risk and return off investing in Apple with the risk and return on my way . And they were supply portfolio that also includes Apple or a similar company from the formula. This simple here ever since the return of the West. If I portfolio, we just need to determine ion diversified portfolio to compare apple trees. You can use the S and P 500 to represent this diversified portfolio. If you have a portfolio of multiple assets like the one, be happy and earlier isn't be 500 in a bone phone. Use that instead as long as your portfolio includes company like apple and it's been a diversified, you know. Example, we've been used the S and P 500 to be the diversified portfolio there is created will still be the sort of etiquette off deposit, same as we haven't used in our previous examples before. Calculating the better value of Apple visual first go over the capital might get line and the security market like 11. Capital Market Line: computer market. The line displaced risks and returns from combinations, off risk free assets and a well diversified portfolio. The diversified portfolio shall include all sectors in the economy. Now, generally two men steps in portfolio management, one maximizing diversification and to decide on September level of risk the diversify for foreign or is the fundament off capital asset pricing Modern We're diversifying for four notion already have included the asset the investor is considering investing in as a making extra element for as the A equal to zero for a well diversified investor toe. Want to include Angelyne weight off asset A in his or her part for No, the risk premium needs to be satisfactory. To illustrate the capital market line, we will start by making difference combinations off S and P 500 the risk free asset the same move we did when we were driving an efficient frontier consisting off combinations off stocks and bonds. We will use the same layout. Copy this area here pissed shake the text s and P 500 this creep changing of formula with off the S and P 500. We're primed by the arithmetic return off the s and P 500 plus with off the risk free asset with a prior by its return press F four here and here Direct down the formula Since we're combining the S and P 500 with a risk free asset, the standard deviation would only be with off the S and P 500. When the pride by stone operation off the S and P 500 press f for here Break down the former and move this a little. We will insert the data into a craft Here, insert sketcher This one select data and seamen I expect you will be too stern off division . And why were you been Veeder return at some liberals and this is the capital market line It chose risk and returns from combinations off risk free asset and the worse If I put for low, you know, case the s and P 500 The point off the carpet on market live. The higher Sharpe ratio is where you hold on lead the the worst by poor for no Here. This is the highest return from taking one extra unit of risk. The difference between the capital market line and capital R location line that we have met earlier in Capital on location line. It chose combinations between the risk free asset with our risky portfolio in our example in their escape or for low waas the stock for for low and I'm born fun. The point with high It's Sharpe ratio is where you have 71% off your cap, it off in the stock for formula and 29% in a bond fund and zero in the risk free asset escape the highest risk and return tradeoff. Capital market lying shows combinations between the risk free asset with a diversified portfolio. The point with the highest Sharpe ratio is where you only hold the diversified portfolio. This is where you have the best risk and return tradeoff. 12. Deconstructing risks: Let's take a quick look at risk in the financial market market. Risk our systematic risk. This is risk from being in the financial market like when changes in interest rates, inflation and order. Economic indicators affect the stock price of a company. Mysteries are not diversify, were business risk or are systematic risk. This risk are from you investing in a specific industry or sector, like when there are new competition in the market or new technology introduced that can reduce profitability off the company you are investing in literacy are diversify able, systematic risk and are systematically are most element in captain credit. Risk off borrower and I want to make the payment liquidity risk disassociated from bad liquidity refinancing risk the borrows ability to repress the existing loan. High refinancing risk will give a bad fisher off look from your investment operational risk . Respond. Bad decision making in the day to day business of a company. Systematic risk result. The financial stability in the society to collapse, political risk consequences from political decisions. The former are for completing the an systematic risk in a stock is my fighting the difference between the total risk, often asset and the systematic risk of an asset and to find the systematic risk you move the product stocks beta with the standard deviation of the market. Let's look more into this. In our example, apperance had a total risk, which is the wear ends and start observation off 0.96 and 31%. Let's plot apples worries into our graph select data and happen. Ex Meru is the star, not division. Why Red Arrow is the writer there? The vote on the risk off Apple is it started out division, which includes the systematic and unsystematic risk. We can even spread this my making a line in search shapes from zero star, not division to happen. Istana division off 31% Apperance Systematic risk. The known there was a five minute risk can be illustrated by making a line from zero started on innovation. But we don't yet know the value of Apple systematic risk. So we will just draw the line up to the markets risk. In this case, doesn't the 500 off 15% Apple's business risk or there was a five on the risk will be the line from happens systematic risk two apples thought on risk, 21%. So the blue line here his happens. Total risk, you know, line is it systematic risk? And the red line is the unsystematic risk off happen. So holding the market for for no or a wind diversify perform no in this case, and the 500 reduces the unsystematic risk from holding only Apple stock equals to this red line here, though in the return also reduces from 21.9% toe only 9% a year. 13. Security Market Line: security market line shows the relationship between the expected return and the market risk . The expected return is the risk free rate plus a risk premium. The risk premium will need to be adjusted for the assets. Sensitivity to the market risk and better represents an assets market risk. Let's illustrate this at a role here. Better better represents the market risk. The risk free asset has better off zero because it doesn't have any relation or correlation with the movement off the market. The S and P 500 is better. Is one because these ever since the market, the former afford a security market line is the same us that kept him for Maura, the K here is the required return, which consists off the risk free rate plus our risk premium. The risk premium is concrete by multiplying markets, excess return with the better off the market. We start by sitting up random better values for now, just up to value one. So zero 0.1 and up to one right that kept him form right here. It's really rich, plus markets access return when the pride by the better off that be had set them with the beta value off. Zero the require it. It is only the risk free rate myth. No risk premium Direct down the former and brought the daytime talk graph Insert Charge Skinner Siddiq. Ditto and security market lying The expert who will be the better and why? Where is the required return has moved us closer to our autograph. So this creates are lying similar to the capital market line that we made earlier, but instead Austin activation. The X value is now showing better. Well, you. This line is called Security Market Line. It shows the require return from an investment for each units off the market. Risk or better, my meta is equal to one. The required turn is the same US. The markets return 9%. Let's just at some labor. 14. Beta: stocks better is its sensitivity to the volatility from the market better while you off Money means the stock price coordinates with the market better off minus one means the stock price moved the opposite way and then the movement off the market, meaning it has really raw sensitivity to the systematic risk. Better over one means it has high sensitivity to the systematic risk the former for better is co awareness between a stock in the market. The white, by the way, rinse off the market. Basically, it is the coordination between a stock and the market. Multiply by start activation off the stock in relation to the market. Stun activation. Correlation between a stock or a company in the market. Various depends on which market you are using us reference and how diversify these market is. Start on division off a stock or a company in the relation to the market. Start adoration ready? It depends on the market and how diversified it is. Furnishing toe how the company is structured like the cost structure in the death level. Let's conquer it better in the spreadsheet even used the former where we take the coherence and divide by the where it's We have already gone through how Corrine is completed and how to use the spreadsheet to complete it. So when you take the coherence between the S and P 500 upper divided mind the wearing off the S and P 500 this gifts empress mate, are to be 0.919 You can also use Excel, former slope, toe konkle it better slow. Take the returns off Apple and the return off the S and P 500. This is better upset. 0.919 Sam value as we completed earlier. Now that we know Apple's better, we can complete the unsystematic risk off Apple using this former The unsystematic risk is the difference between an assets Donald duration and an asset systematic risk. The systematic risk is concrete by multiplying the assets better with the start duration off the market. So Apple's better with the pride by it's not division off the S and P 500. This gives the systematic risk off happen, Toby 14% and the unsystematic risk it just the difference with me. In happens total risk off 31% miners The systematic risk This gives a systematic risk. Ops 17% 15. Alpha: are far is the measurement for mispricing. Basically, the UN for well tells you how much and assets return deviates from the return completed through kept him and the security market line are for well, you off. Zero means the effort is correctly priced very over. Zero means the assets has an unusual low price. Why are far value below zero means death is overpriced. The reason for mispricing can be due to many different factors like how Ah, quit or representative are out model and data going back to our first question at the starts off this section, we ask if happens return. It's worth its volatility since we now have all the well we need. You know, Captain, more than formula, we can congregate. What happens? Return should be according to kept him be at the rule here. Kept him, we take 30 Sphere Ranch, plus the excess return from the market adjusted for Apple's beta. This gives the required turn off 8.53%. We find the difference between apples historical return and they require return covered it . The bike kept him this cape 23 1 32%. This is the Alfa Whaler which means that Apple's outperforms the market by 23.32% and that the stock is under price according to cover town pricing model. Plus the wrestles into our security market like graph. But I think select data and ex very will be Ephron Sabetta. Why were you? I mean the happens alpha and some neighborhoods, the so everyone has a better return than what is required for the better wire that it has. Assuming that the investor can be was if I AP runs on systematic risk off 17% the stocks returned is worth its systematic risk off 14%. Let's notice to all of the stocks we have gone over in this course as we were asked them bone fun. So you take cold bearings between Amazon and S and P 500 divide by the where it's on the S and P 500 coherence between Google and S and P 500. Well aware events isn't the 500 same for Microsoft Bush I and the border form there . The wrestles are in the same us. For example, in Yahoo finances. This is new to the sample. The Open has used three years monthly movements to concrete the better. We have used yearly movements off 10 years even be up to you. How far back you know that are should be. It would choose what is the representative for your investment horizon and also the rest of the values. So look this, I said and just direct the former look, This cell, this one and it's on direct the former no, there. So we add some rolls here, powerful, new and will deprive. We need to move the prime. The assets Beta is there with in the portfolio you can use in multi formula For that in most multiplies to a set of area. The first every must mean a role for that. And the secondary must be in a column for control shift. Enter there. We can plot this into our SML graph Select data and but one do X value of inveigh. Our performance in Beta and Riva new therefore okay there doing the same thing for the stock and born put for new that we had congregated earlier. So take the with off the stock for for low, well deprived by the better off the stock for for you plus the wit Oh, the Bond Fund. Wonder pride by the better on the bond fund 20 hour Far the wet on the stock for four years with applied by in the Alfa Plus we have a lot of bone Phone one deprived by the alpha There plot the results into oh graph select data Dead stock and bond expenditure would be the better. Why, when will be the hour for Okay, Okay, At the 11th and short title it's the middle there and now we have the over off the alpha and better for apple the stock for for no, let me construct in previous section and the stock and born for follow that we also construct In previous section off this course, all three had the returns higher than cabins require return But remember, you still need to be able to diversify their unsystematic risk 16. Diversification through global portfolio: What if we want to consider in the OneWorld as now investment opportunity even start by making a covered on market line craft that includes the probe on for for you combined home and groping for four nos complicating the return and stand operation and brought them into the graph. The advantage of investing in the program for follow will be equal to the difference between the return from combining home and Groban for follower, and they returned, calculated by using kept him as showed in the former. The former rock tells us that it will be more preferable to diversify through investing in the Groban apart for Law only if the to four follows have a negative correlation. Which issue order. Here we have the price movements for the actual stock's exchange. This will represent the home portfolio. The problem portfolio will be the S C. I will index e T F. This is an idiot that replicates the performance off the World index. We calculate the historical returns and volatility the Norwegian Treasury notes off 3 to 10 years, happy to be in 1.15% to 1.8%. They're going represent their spirit, but the rates are so low that it is better to use the bank deposit rate, which is also quite risk free 2.30%. It's colonel in the Hyatt saving account rate in Norway and we had a witness section here. We will make cover, turn market line graph and start vice Setting up combination between the global for for no and they risk free asset concrete the return the ways off the crowbar for folio with the return across the with off the risk free as it with the fire By the return direct down the formula are not division. You take the with off the portfolio with the pride by its star, not duration. Direct down the formula and we make a graph Insert shot skater Siddiq dead are and resort market line X value invaders started on division. Why were you is the returns move this shower? Yeah, and some labour. This is the combinations between the Groban for for low and the risk free rate off the home market. The point with the best tradeoff between risk and return is where you only home the Groban portfolio to see it is better to diversify your investment toe the globe on put foreign or when you are investing in Oslo Stock Exchange, you start by combining or snow our homeport for no with the program for for no with the combination so that the sharp glacier it's makes it might. So we set a random wet first. So 50% here. A person? Yeah. Co Creator Sharpe ratio sharps ratio is the price for ish unit of risk. So you take the return on the portfolio miners there is free, right? Oh, uh, the standard deviation. Let's try using a silver toe. Find the location that gives highest return pie units of risk. So data so number. You set this settle to a maximum by changing these two cells and keep this cell upto 100%. Okay, so, okay, it shows that visual only invest in the global portfolio. Austro Stock Exchange has to high risk for the return. It gives for the sake off this example even keep the allocation as 50% in a portfolio flocked the data into the computer market line graph Select data and but photo expander is their star, not division. Why Manu? He's dirty. Turn at some neighbors we can already see that Oslo stock exchange make the portfolio more risky for the same return. Let's break down the risk of Oslo stock exchange by calculating better for simplicity. We will use the slope formula. So school using the returns from Oslo stock exchange over the return. Oh, the global portfolio Completing systematic risk. What's knows better multiplied by Mr Not duration off the Groban for four years. Our systematic risk It just the difference between or slow stunned out division and no systematic risk. The required return. You just called me the captain former from here, pissed safe. This cell promising p 500 to the return from the group are performed and on far is the different Syrian arsenal. Historical return and Oslo's require returned from Captain E News The decimal so also has quite high systematic risk. This is on on diversify even risk are five value is negative, implying that Oslo stock exchange is overpriced, comparing to the global portfolio and to find if there is excess return by diversify and combine your investment with a Groupon portfolio. We take the return from the combined portfolio minus Oslo Stop issuance to require return cold weather might kept him reduce the sitting decimals. This shows that for a Norwegian investor who currently invest in Oslo stock exchange index once again, any excess return by diversifying through, for example, 50% in Groban portfolio. This is because Oslo Stock Exchange has high sensitivity. So the global economy with unknown diversifies the risk off 14% when it's total risk is 16% . And that's it for the section about the capital asset pricing more Thank you for washing. 17. Conclusion: we have gone through how to conquer it. Risk and return sitting up a part for low finding minimum variance portfolio. Construct apart for no that maximizes Sharpe ratio. Construct on optimal our location between the risky asset and risk free asset, how relativity awards over time and how to complete the expected return using capital asset pricing. Mortar, as mentioned earlier, This cost for lost the work off. More important for low Terry and the capital asset pricing model is built upon that work. It shouldn't be used together with your daughter. Investment two words When using what you have learned in this course to fire an investment opportunity, which are also look at other factors like expected returns even expected return is based on the history comprised movements. Consider how far back in time surely data be. This depends on what is the representative and your investment horizon. Even even expected. Return up. A company is positive or negative if one student to an intensive research off the company like looking into the sector and income statement, and that's it for this video course. Thank you for washing 18. Tests: here is the closing stock price off the the Value Offshore, a company that operates in floating production storage. It is listed on Oslo Stock Exchange, so find a yearly return on the stock. Using the historical returns was arithmetic and geometric. Assuming the exchange traded fund for the utility sector and the industrial sector have the following year, religions and variants, 11% returned for the utility, with various off 0.62 and 20% return for industrial and 0.2 for wearing. The coherence between these two sectors is single 20.1 night. Construct a minimum variance portfolio. Find the portfolios expected return and start not deviation. Same assumptions as the previous test. Using the 10 year Treasury bill read as the risk free rate. Construct a portfolio that maximizes the shaft ratio. What is the portfolio's return and stand up deviation? An investor believes there is in return from the S and P 500 to be representative for investors. Expectation assumed that the S and P 500 has a yearly return off 9%. Where is off 0.23 estan a deviation off 15% 10 years. Touching tribute off 3% is the risk free rate. Assuming former for the proportion in the risky asset holds true for maximization off utility. If the investor wants to invest 100% obvious capital in the S and P 500 what is being Mr three? Solution? Cough isn't how much does the pressure Bilbray has to rise to before there? Mr reduces the exposure from 100% to 95% assuming an investor has 50% invested in XLK and 50% in X TL. XLK has a yearly return off 18%. Willian's off 0.71 Extell has a 9% return, wearing off 0.74 Coherence between these two TDs is minus 0.3 What is the expected return and start division off this portfolio? Assume further that the investor can borrow from his broker to invest it in Mr Want a standard division off no more than 15%. How many times a piece capital can he borrow 19. Tests and Solutions: here is the closing stock price off the value Offshore, a company that operates in floating production storage. It is listed on Oslo stock exchange, so find a yearly return on the stock. Using the historical returns was arithmetic and geometric To find a return off a given year . Your take the price off that year or the price on the previous year, minus one on direct down the formula and then concrete the average tape 11% enigmatic average Return for a geometric mean. You find the interest factor for each return by adding one so and use the deal mean former to concrete, the average minus one. I took a word. The data back to the original skill some minus 10.2% geometric mean assuming the exchange traded fund for the utility sector and the industrial sector have the following year. Religions and variants, 11% returned for the utility, with various off 0.62 and 20% return for industrial and 0.2 for wearing The coherence between these two sectors is single 20.19 Construct a minimum variance portfolio. Find the portfolios expected return and start not deviation. So we will use this form row. We take the wearing off X I minus Korans. Divide by where is off utility plus Americans are industrial minus two. Multiply by in the coherence. This gives at the 4% in X and a new and 16% in X and ally, and the return would be else the wet off in the sterile with the pride by that in turn 7.63%. And where wins, we just use thes form, you know, take the wet rise by two. Well, the prime by the weapons with us. No red in the steering right to, well, the provider where rinse plus toe on the prime by the with and wonder prime by the coherence. This gives the reverence off 0.54 It's done on innovation 7%. Same assumption as the previous test. Using the 10 year Treasury bond with us, the risk free rate construct apart for loan that maximizes the shafts ratio. What is the performer's return and standard deviation? We will use this formula here toe concrete, the shop ratio. So in the return off, the California miners the risk free rate the wire binder star, not duration on the portfolio escapes the sharp pressure off 1.163 We used the start of a function toe. Find the allocation that gives higher Sharpe ratio. So did I. So set this cell two Mex by changing these two cells, ending constraints where this seven is equal to 100% some. Okay, So to get hired shop ratio, you should have 60% on your investment in the utility sector and 40% in the industrial sector. This gives 14.4% return. It's percentage stone on division and 1.316 Sharpe ratio on investor believes the risk and return from the S and P 500 to be representative for the investors. Expectation assumed that S and P 500 has ah yearly return off 9% where is off? 0.23 and standard deviation off 15%. 10 years. Treasury gone off 3% is the risk free rate assuming formula for the proportion in a risky asset holds to form s immunization off utility. If the investor wants to invest 100% off his coverage on in the S and P 500. What is the investors? Risk of washing cough isn't. How much does the Treasury bond rate has to rise to before? In Mr Induces, the expulsion from 100 percent to notify. Present, even start from this former, we have all these sweaters. We want to find the well off their risk aversion. Coffee isn't the letter a here? So we take this value here. Wishes the return on the portfolio minus the risk. Free Red. So nice person minus 3%. And we divide by this better. This is the proportion in the S and P 500 there which gets us this way. See the point 06 And then we divide this man who with the way Reince, which is several points in a to three and then be a divide this value is to get the rest of Russian Corp isn't so to this gives The dissolution club isn't off 1.0. So let's test it. We interned a risk aversion, Corvis in one point, Casero there my mother percent in the s and P 500 Now, to find what there is clearly it has to be before the investor reduces the proportion in the S and P 500 from 100% to 95% using the same former. They want to find this value that gives this very 95%. So you just take little 0.95 or 95% well deprived by this very we already con created this value previously to be a 0.6 There this give us this mirror so that you just take the return 5% minus this video. And this gives us this matter that gifts this better 95%. So being searched the 3.3% here there then Mr Reduce He's exposure from 100% tonight of my present when the risk free rate increases from 3% to 3.3%. Assuming an investor has 50% invested in xlk and 50% in X tl, xlk has a yearly return off 18% where Ian's off 0.71 Extell has a 9% return. Where is off 0.74 who warrants between these two idiots is minus 0.3 What is the expected return and start division off this portfolio. Assume further that the investor can borrow from his broker to invest. Even the investor wants a standard division off no more than 15%. How many times a piece capital can he borrow? Contradicted return? Just take the way multiplied by the return. 13.5% in the weapons. They just follow this former. So the way I spent two with the prime, by the way, rings just with my to the Where ends Chris to will the prime by the with and with the Prive Ide the coherence this Get the weapons off 0.2 and stun on division No by prison, the investor ones normal and 15% standard deviation. How many times off his capitan Kenny borrow? So you just take 15% over Istana division on the portfolio. This gives 325% so just take miss minus along. So basically he can borrow two point 25 times off his capital