 Hello and welcome to the session. This is Professor Farhad in which we look at asset allocation across risky and risk-free asset portfolios. This topic is covered on the CFA exam as well as essentials or principles of investments, graduate and undergraduate course. As always I would like to remind you to connect with me on LinkedIn if you haven't done so. YouTube is where you would need to subscribe. I have 1800 plus accounting, auditing, tax, finance as well as Excel tutorial. If you like my lectures, please like them, share them, put them in playlists. If they help you it means they might help other people connect with me on Instagram. On my website farhadlectures.com you will find additional resources, the complement and supplement discourse as well as your other courses. So to start this session we want to be familiar with some basic concepts. Some of them are new, some of them you have already seen but I want to make sure you are comfortable with them. The first one is asset allocation. So what do we mean by asset allocation? It's a portfolio choice among broad investment classes. For example, you want to invest in stocks, you want to invest in bonds, you want to invest in money market, you want to invest in treasury bills, those are broad investment classes or you or we have something called capital allocation to risky asset. Now it's the choice between risky and risk-free asset. So for example, the T bill is risk-free, money market is considered risk-free, stocks and bonds are considered risky asset. So the question becomes in the capital allocation stage is how much do you invest? For example, do you want to do 60, 40, 50, 50, 70, 30? It's what percentage do you want to allocate to risky asset? Complete portfolio is the entire portfolio including risky and risk-free assets. So when we say complete portfolio it includes both whatever we chose in this stage. Risk-free asset is the asset with a certain or guaranteed, I'm going to put guaranteed in quote guaranteed return. It means there's no issues with it. And for the purpose of my course we're going to consider the US government treasury bills as a risk-free asset benchmark. Now there are two other terms you need to be familiar with for this session we already covered. One of them is the sharp ratio and it's the ratio of portfolio risk premium divided by two the standard deviation. This should be a review for you and we need to look at risk aversion which is the reluctance to review to accept risk. You can review both of these ratios which is this is how we compute the sharply ratio which is the risk premium divided by the standard deviation and the risk aversion which is is computed by by the symbol A. It's the risk premium dividing by the variance. Now the reason I am mentioning those two topics here although we looked at them in the prior session you can see the link in the description is because we're going to be using them at the end. After we select the portfolio we need to select how are we going to allocate the risky versus risk-free assets so that's why I want to do that. So you have to we always have to remember I mentioned this in the prior session that you always you have to make a choice between risk and return so it's always good to go back to this basic common sense concept. If you stay home and you don't do anything if you take no risk you should not have any return but as you take risk if you are a reasonable person one level two level three level four full level of risk you expect your return to go up as well and let's assume one for one notice risk is risk and return they're positively related the more risk you take calculated risk the more return you would expect so keep that in mind always when we are dealing with finance okay so given the available trade-off between risk and return there's a trade-off the more risk you take the more return you expect which is common to all investors each individual can choose his or her preferred allocation between risky portfolio and risk-free assets when you are when you are preparing your portfolio do you want it to be 60 risky 40 risk-free do you want it 50 50 so on and so forth so you have to choose the choice depends on your personal preferences and specifically the risk version that we talked about in the prior session which can be computed but the best way to illustrate this is to actually work an example to see how we build a portfolio so let's assume we have a risky portfolio we're going to call it p we're going to allocate y to the risky asset and y minus 1 to risk-free asset so basically y is everything that we have the total budget we're going to allocate some of it to risky asset and whatever whatever's left is to risk-free asset so if we allocate it 60 to risky asset what's left is 40 percent and we're going to we're going to show the actual risky asset of return on the portfolio is the risk of the portfolio the expected rate of return for our portfolio we expect to earn 15 percent the standard deviation it's going to be 22 percent the risk-free rate is seven percent therefore the risk premium is eight percent which is 15 minus seven which would give us the risk premium for this portfolio of eight percent now what we're going to do we're going to we're not computing we're going to draw the capital allocation line given this portfolio now what is the capital allocation line let's look at the definition then we would look at the port we would look at the picture itself basically what we're looking at is plot of risk return combinations available by varying portfolio allocation between risk and risk-free asset and risky portfolio now the best way is for me to start to build this for you remember we have return and we have risk we have return and we have risk and we're going to call the the risk now the standard deviation so the standard deviation for us is 22 percent and we have the return you know on the y-axis so this is the x-axis this is the y-axis now here's what we can do we can just take all our money and invest them in the treasury bill and earn seven percent so by doing so treasury bill has zero risk we can earn seven percent without doing anything without taking any risk this is what we what what I mean by not doing anything that's one that's one option all the money that we have all of y it will be 100 percent invested in here therefore we have an we have a point here or here's what we can do we are risky people we're going to take all the money and invest it and our expected return is 15 percent but at this point we're going to be taking this is the standard deviation is 22 percent therefore the point they will meet some place here so this is the other extreme the other extreme is invest all the money in risky assets okay so let's draw the line between those and this is what our capital allocation line would look like now are these the only two options that we have absolutely not guess what I can take half of my money invest it in in risky asset in risky asset and the other half I want to invest it in risk free asset what will be my expected return if I did this if I split my money 50 50 so why is 50 50 well here's what happened for my for my first 50 percent for my first 50 percent it's going to be invested at 7 percent and for the second 50 percent I expect to return of 15 percent so here's what's going to happen 50 percent 50 percent times 15 percent that's going to give me 7.5 and 50 percent times 7 it's going to be give me 3.5 3.5 plus 7.5 is 11 percent so here's what's going to happen if I put 50 50 I'm going to be earning around 11 percent and my and now my portfolio standard deviation I will show you later it's going to be also cut and have 11 so basically I will meet here in the third portfolio so notice any combination I make I'm going to fall along this line so even if I do 60 40 if I do 60 percent risk free and 40 risky I'm going to fall someplace on this line so this is what we mean by capital allocation line so any combination I I undertake it's going to fall on this line and you notice the extreme if I put everything in my in the treasury bill or if I invest everything that's going to be on the same line on the same line so this is another picture of what I'm just what I just talked about so here's the here's if I split everything 50 50 I'll make approximately 11 percent and the standard deviation will be 11 percent if I invest everything this is p it means I'm quite risky f I'm very conservative and the sharpie ratio s equal to eight divided by 22 what is eight eight in this portfolio is the risk premium risk premium if I take the risk premium divided by the standard deviation which is 22 I'll get much I will get my sharpie ratio we'll see that in a moment but this is what the capital allocation line looks like now I can also invest more money that I have by borrowing which will will work an example and they have at the end of this session to show you if you use leverage how do you compute this but anyway if you use leverage you would still fall along this line along this line the capital allocation line now the so let's just have some general statement about this capital allocation line the first thing is the risk premium of the complete portfolio equal to the risk premium of the risky asset times the fraction of the portfolio of course the risk premium it's going to be only to the portfolio because the risk free has no premium the risk free is does does not have a premium so it's the portion of the portfolio that's invested multiplied by the risk premium which is the expected return minus the risk free also the standard deviation of the complete portfolio it's only equal to the standard deviation of the risky assets times the fraction of the portfolio invested in those risky asset of course that's the case because the risk free assets don't have a standard deviation they have a standard deviation of zero so if we invested 60 percent in risk free asset and 40 percent in in in risky asset this 60 percent will have a standard deviation of zero which will give us 60 then the remaining 40 percent wherever the standard deviation fits 22 this will be the standard deviation of the portfolio simply put the standard deviation of the portfolio is only composed of the risky asset of the risky asset just stuff you need to be aware of we can generalize the risk premium which is eight percent and the standard deviation of the complete portfolio increase in proportion to the investment in the risky portfolio and this should make sense from the from the sharpie from the sharpie ratio the risk premium and the standard deviation increase in proportion to the investment so if you want to increase your investment you want to increase this increase your risk you'll increase the sharpie portfolio but let's take a look at the different portfolios the first portfolio we said it's expected return is 15 the risk premium is eight the standard deviation is 22 also if we want to compute the sharpie ratio it's going to be eight which is the risk premium divided by 22 equal to 0.36 now with the portfolio c the expected return is 11 when we put 50 50 the risk premium is is four percent why because it's 11 the expected return 11 minus 7 will give us four percent seven is that is the risk three and the standard deviation is 11 again if we take if we'll do the same thing we'll take four percent divided by 11 it's also going to give us a sharpie ratio of 0.36 simply put the sharpie ratio is will give you the same as long as you are on this capital allocation line the next question is what is the best how can we find the best allocation so this is we can be here we can be here we can be here we can be anywhere on this line the question becomes what is the most the best allocation on the risky portfolio well think about it before we kind of look at the answers it all depends on the risk tolerance of the individual okay if the individual can tolerate risk we will be our portfolio will be closer to p or p is the maximum if if the on the other extreme our investor is has a risk does not have risk tolerance risk totally risk averse we all portfolio will set enough or it could be some place along this line but we can measure this we can measure where should we be based on the risk aversion and the sharpie ratio so investors degree of risk aversion a this is what we looked at in the prior session measure the price of risk the individual demands from a complete portfolio in which her entire wealth is invested so we're going to look at the degree of risk aversion and the compensation for risk demanded by the investor must be compared to the price of risk offered by the risky portfolio what is the price of risk this is the sharpie sharpie sharpie ratio so we're going to look at these two ratios together so we can find the investor preferred capital allocation which is you know how much invested in risky asset and risk free asset by dividing the risky portfolio price price of risk which is again sharpie ratio and and by divided by the investor's risk aversion divided by a and simply put this is the equation we're going to look at the we're going to basically look at the sharpie divided by a that's basically what we're looking at and we're going to get a number and based on this number we're going to see how we allocate the fund so let's assume we have a price risk of two so the sharpie ratio for our example is two and the risk aversion is three point nine one three point nine one here's what we do now we'll take two divided by three point nine one and we'll get point five one it means based on this individual risk tolerance and the price of risk based on the standard deviation we would and would invest notice 51 almost 50 50 51 let's be more specific 51 percent and risky asset it means we're going to invest 49 percent and the 7 percent which is the risk free asset this is what we mean by that now we have to understand how these two these two ratio these two numerator and denominator work together the optimal allocation to the risky portfolio is directly proportional to the to its price risk which is the sharpie ratio simply put let's assume you increase the two to three point nine one so i make it three point nine one to show you it's going to increase it's going to give me easier math so if i increase the numerator the shot of the sharpie ratio increase the three to three point nine one divided by three point nine one now i invest everything in the risky asset the answer equal to one it means 100 percent and risky asset so you so the first thing you want to know is if you increase the numerator which is the which is the sharpie ratio the price of risk the risky asset will go up however it's inversely related to the investors risk aversion now the opposite is the opposite will happen here if you increase this from three point nine one to four this is going to go down to exactly five now it's 50 50 so notice it's the risky asset are directly proportionate to the price of risk but they're inversely related to the risk aversion make sure you know this relationship how it works and what makes it makes it more sense make sure you go back to the prior session and see how we compute the price of risk and the risk aversion that's very very important to kind of makes it easier for you the last thing we're going to do is going to we're going to look at an example where we use leverage and try to make more sense out of it because i showed you in the when i was illustrating this model that we can be beyond why why can't be more than one so just let me show you the graphs because i told you here we're going to come back and say why is more than one one point two five you know what does that mean it means we borrowed more money than what we have okay but we'll work an example illustrating this concept so let's suppose that the investment budget is 300 000 and investor borrows an additional 120 so basically we borrowed an additional 40 percent because 120 divided by 300 000 is 40 percent so we have 420 000 so why the total money that we have is not one y equal to 1.4 because we borrowed money we borrowed money in additional 120 000 now one minus y okay one minus y is 1.4 equal to negative four what does negative four means negative four reflect a short position in risk-free asset short position means you borrowed money because you have to when you have to pay something back that means you are short you have a short position you have to pay it back it's like a liability or a borrowing position so you have 0.4 which is a dollar amount 120 000 but just kind of since we are using percentages so rather than lending money at four at seven percent the investor here borrows the money at seven percent with the weight of 0.4 this is why this is important you're going to see why the weight is important why are we saying 0.4 and risk-free asset and 1.4 in risky portfolio so simply put here's what we did we borrowed money because we borrowed money that additional 40 percent we have to pay on it that's an expense but that borrowed money it's going to go and add it to our y so now we have 1.4 y equal to 1.4 and that 1.4 it's going to be invested in in quote high return so hopefully if it works well for us we'll do better because now we have we're going to pay risk-free return which is low return and make a higher return hopefully that's what's going to happen so simply put our expected return should go up why now we have seven percent times negative 0.4 notice it's negative 0.4 times seven percent because we're paying money so notice here it's negative plus now we have 1.4 the always has to equal to 100 1.4 minus 0.4 equal to 100 so the weight has to equal to 100 but now we have 100 140 percent multiplied by the expected return of 15 and hopefully already figured out that our expected return is no longer 15 percent for this portfolio our expected return is 18.2 why although although we thought it's 15 but since we are leveraging our expected return will go up will be higher so our expected return for this portfolio is 18.2 and the reason is because we borrowed money at seven and we think we're going to make 15 percent on it but we have to pay back the seven and what's left will be profit and as a result it will increase our return to 18.2 so that's why our return went up now another way to compute this another way to compute this is to is to do it through the dollar amount and how do i do so through the dollar amount i am investing 420 000 at 15 percent as a result i'm going to be making 63 000 however i borrowed 120 000 and i have to pay pay back the interest of seven percent on this money therefore my interest expense is 8 400 now what i need to do from my total return i have to deduct 8 400 and as a result i'm going to be left with 54 600 dollar if i take 54 600 dollar divided by my initial investment of 300 000 i should be earning 18.2 percent on this portfolio again back to the same 18.2 what we did is we computed this differently through the dollar amount here here we did it through the weight make sure you know how to do it both ways and make sure you do so it means you understand it okay also what we what we can find out is the portfolio standard deviation remember the portfolio standard deviation is only the standard deviation of the risky asset the risky asset represent 1.4 percent of the portfolio hold on a second it's more than 100 percent that's right because you borrowed money 1.4 times the standard deviation so the standard deviation of the portfolio is 30.8 hold on a second didn't you say it's 22 it is 22 but i leveraged once i leverage my risk goes up remember when you borrow money and you leverage up that's risky that's risky your risk goes up and notice notice here in numbers you see as you leverage your risk goes up how does it go up measured by the standard deviation went from 22 to 30 and the sharp ratio for this portfolio is 11 it's a 0.36 0.36 and again as you might have expected the leverage portfolio has about a higher expected return and a higher standard deviation higher standard deviation than an unleveraged position in the risky asset of course when you borrow money risk goes up risk goes up return goes up notice your return goes up your expected return goes up but your risk goes up as well again back to the idea of more risk more return less risk less return that's the general idea in the next session i would take a look at the diversification and portfolio risk or i might work an example another example that deals with this topic we'll see how it goes anyhow i'm always going to invite you to like the recording share it and don't forget to visit my website farhatlectures.com for additional resources to complement and supplement this course as well as your other accounting and finance courses good luck study hard and stay safe