 Hello and welcome to the session in which you would look at risk premium, risk aversion and the sharpie ratio. These three topics are interrelated so it's very important to cover them all three together. This topic is covered on the CFA exam as well as an essentials or principles of investment 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 1,700 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 benefit you it means they might benefit other people, share the wealth and connect with me on Instagram. On my website farhatlatchers.com you will find additional resources to supplement and complement your course as this course as well as your CPA, CFA, CMA exam as well as your other accounting courses. I strongly suggest you check out my website. We're going to start by looking at risk premium. How do we measure risk premium? So I want you to keep this relationship in mind which is a relationship that makes sense and I hope it makes sense. Let's take a look at risk and return. This is risk on the x-axis and we're going to look at the return at the y-axis. So if I ask you if you take no risk do you expect any return? In other words if you sit home and you don't do anything in your life should you earn anything and the answer is no. You're not risking anything. So if you have let's assume a thousand dollar and that thousand dollar is in your mattress what are you risking? Nothing, nothing therefore you should not earn anything. Now what can you do? Well what you can do is you can take this one thousand dollar and take it to the bank or buy t-bills with it and you're going to see why I said t-bills short term treasury bill. Well if that's if that's the case you're really still not taking any risk whether you have that money in the bank or if you bought a treasury bill basically your risk is zero but you might make maybe I'm just going to say two percent. So if you invest this money you are still taking no risk and you'll be up at two percent here so risk is zero you earn two percent. Now here's what happened your friend might come to you and he or she might tell you look I have this business idea do you want to invest with me? Well guess what that business idea will carry risk or you might want to invest this money in the stock market or you want to buy real estate or you want to buy gold. So here's what's going to happen as you steer away from the bank and from treasure by treasury bill which is once you steer away from safety okay so once you start to take more risk okay what's going to happen as you take more risk logically speaking you want to earn a higher return. So let's assume you your friend wants you invest you want to invest your money with your friend. Well you don't know much about his or her business but you want to earn to be on the safe side you're taking more risk as you take more risk you may want to earn ten percent ten percent so your risk is here and ten percent is here or you might want to buy a stock with a with a drug that's unproven yet so a drug under FDA approval well you're taking more risk because it's under FDA approval as you take more risk you expect to be compensated maybe at 15 percent at 15 percent you'll be compensated here so here's what happened here's here's the relationship that I want you to keep in mind as you take more risk you expect more return so risk and return if risk goes up if risk goes up if you take more risk you expect to be compensated and I hope this basic idea makes sense to you because this basic idea is very important for this session so this is the basic idea behind this session the first thing we're going to talk about in the find is something called risk premium and what is the risk premium it's the difference between the expected holding period return hpr on an index fund and the risk free treasury bill that you earn with certainty so if you put your money with the government in a short term treasury bill you might earn let's assume this is two percent well this is risk free because you've really taken no risk you're going to earn this this this percentage but if you invest your money in the stock market you might earn in the stock market 10 percent so this whole thing is 10 percent now guess what the risk premium the risk premium you are taken is let me use a different color here the risk premium you are taken is eight percent so the difference between your expected return your expected holding period return which is 10 percent and your risk free guarantee rate is your risk premium so by undertaking this investment you are you are getting a risk premium of eight percent because if you don't want to you can make guarantee two percent so if the risk free rate and the in the example is four percent and the expected index fund return is ten percent so basically let me just show it to you here in boxes so this is the treasury bill will give you four percent but if you invest in the index stocks you're going to make in total in total ten percent therefore the extra six percent is the risk premium is the risk premium so i just want to make sure you understand this idea because we're this is a powerful idea another term that we use is access return which is the return and access of the risk free rate so anything you earn above the risk free rate which is we're going to be using the risk free rate treasury bill short term treasury bill is called access return so simply put for for my purposes you could use the access return and risk premium interchangeably now from the risk premium we're going to talk about risk aversion what is the risk aversion risk aversion is the reluctance to accept risk as individual we are risk averse in other words we try to avoid risk as much as possible if we want to take risk remember remember if we want to take more risk what do we expect we expect to earn a higher return so yes if we're going to take risk we're going to we're going to expect a higher return but generally speaking we can say we are risk reluctant okay we we reluctant accept risk so risk risk aversion is the degree to which investors are willing to commit funds to stocks depending on the risk aversion how much you're going to invest in stocks what i mean by stocks risky investment it doesn't have to be stocks it can be real state it can be your friend asking you to asking you to invest under under new invention that's that's that's risk it all depends on your risk aversion investors are risk averse in a sense that without positive premium risk premium they would not be willing to invest invest in stocks so what is risk premium positive risk premium positive risk premium is that extra above the treasury bill rate above you remember the four percent treasury bill you only would accept risk if they can if you are compensated for this extra premium so in theory okay there must be always a positive risk premium on risky asset in order to induce risk averse investors to hold the existing supply of the asset otherwise you are a gambler think about it if you don't believe risk and return comes hand in hand why would you invest well the reason you would invest because you are gambler so simply put you would always you want to have you want to have that extra risk premium so again i'm gonna i do this several times but there is a reason for it so if the treasury bill is paying four percent for you to own the stocks you you should expect a return of ten which is an extra six percent so you would only take the extra risk only if the expected return is higher otherwise we will not take that risk okay now to determine an investor optimal portfolio strategy we need to quantify we need to put a number on that risk on the degree of risk aversion so we need to measure the degree of risk aversion so an obvious benchmark is a risk-free asset so basically we look at the risk-free assets which neither have volatility nor have risk premiums if you invest in risk-free asset what is your risk you have no risk whatsoever why because the risk-free asset like the treasury bill or a cd in the back cd in the bank has no no risk premium and it doesn't have any volatility so it pays it pays a certain rate of return if it's a risk-free or an f risk-free risk averse investor will not hold risky asset without the prospect of earning some premium above risk-free rate again back to this idea that you only invest you only invest if the return is worth is is is the return is above the risk-free rate that's the only that's the only reason we infer higher risk aversion if we have demanded higher risk premium for any given level of risk well what does that mean it means if i want to take more risk i want more return that's basically what it means i want a higher risk premium i want a higher risk premium now we're gonna measure this exactly how we measure this this risk an individual degree of risk aversion can be inferred by contrasting two things we're gonna look at the risk premium on the investor's entire wealth so his complete portfolio let's assume you know his a complete portfolio against the variance of the portfolio so simply what we're gonna have we're gonna take the risk free at the risk premium risk premium which is the expected return minus the risk free divide this by the variance and that's how we measure that's how we measure the risk aversion so the ratio of risk premium to variance risk premium to variance means divided by the variance measures the reward demanded per unit or per unit of volatility so for example if an investor whose entire wealth has been invested in portfolio q with an annual risk premium of 10% so that's the numerator 10% is the numerator and a variance of 0.256 0.0256 not 0.256 0.2056 the standard deviation 16 we're not dealing with the standard deviation for now what's going to happen is you're going to have a risk aversion or a risk aversion equal to 3.91 which is the risk premium which is the expected rate of return minus the risk free rate we're not giving the detail which is basically given the numerator is 10% the denominator is the variance and be careful it's the variance not the standard deviation because we're going to look at the standard deviation in a moment so we call this ratio here risk premium to its variance the price of risk or market price risk so this is how we price the risk and this is important so based on this price price of this risk we would allocate wealth between risky and risk free sorry and risk free assets and we're going to see later on when we start to put a portfolio together and this is I'm sorry when we start when we start to put start to put a portfolio together we want to know what's the price of risk and based on that we will determine the allocation also in the real world when you when you are dealing with a client in the real world when you're dealing with a client the first thing is you want to know what's the how how much risk do they tolerate if they tolerate a lot of risk well you're going to have more risky investment than risk free asset if they don't tolerate a lot of risk then we're going to have less risky asset now what does that 3.91 means just give me one second we'll we'll discuss this in a moment with another example right now assume how do you interpret it that's what I'm trying to say assume a complete portfolio represented by the stock market index such as S&P so let's assume we have a portfolio that's representing the S&P 500 call it M the average access return which is the risk premium on the market is 0.08 so this is the numerator and the variance is 0.04 let's compute the risk aversion or the risk aversion well it's it's said the old or the price of risk if we take 0.08 divided by the variance equal to two now remember in the prior example we had 3.91 now we had two so what what does these numbers mean let me just tell you in general what do they do then we'll change the numbers a little bit for it to make sense conventional wisdom holds the plausible estimate for the value of the price of risk a lie in the range of negative 5 to 4 oh what does that mean let me just kind of quick do a quick computation here and show you what it means so this way you'll have an idea how does the price of risk affect the risk premium as well as the variance in the portfolio how does the variance affect the risk premium so let's assume the same the same information except that our risk premium is 10 0.1 so let's compute if we take 0.1 divided by 0.04 variance not 0.4 0.04 that's going to give us an a of 2.5 now let me just so it's point let me let's compare them hand in hand so we we change the risk premium to 0.1 the variance is 0.04 that will give us an answer of 2.5 if you have a choice between those two portfolios which portfolio will you choose of course I will choose this portfolio right here why because I am getting more premium more return I'm taking more risk without a change in my without changing my variance without changing my dispersion therefore 2.5 out I'll prefer a portfolio of 2.5 and let's let's change this let's assume it's 0.08 I'm earning 8% but my volatility is 0.0 let's make it 0.08 to make it the math easy 0.08 divided by 0.08 is one here's what's happening is I am I am my risk premium is 8% but I am I am experiencing a lot of volatility in my portfolio therefore I would prefer this portfolio over this portfolio so hopefully it's start to make sense when we measure the when we measure this this this ratio the price of risk now hopefully it make more sense so this this is pretty good this this is good but again you have to kind of look at it in perspective you have to look at it in perspective another similar ratio is the sharpie ratio the sharpie is the person that created the ratio William Sharpie now what we're going to be looking at is the that's pretty similar and you're going to see it's the ratio of portfolio risk premium to the standard deviation not not not the variance to the standard deviation so risk aversion well we just looked at implied that investors will demand higher reward to accept the higher portfolio volatility which I just showed you this well same thing I mean all what we have to know is if we have a portfolio risk premium we can divide this by the standard deviation of the portfolio access return so rather than the variance we're going to divide it by the standard deviation that's all what it is the risk free asset will have zero premium and a zero standard deviation because when we're dealing with risky free assets they have no deviation they have no risk there is no risk premium so a risk free asset this is the risk free asset risk free asset is basically it does not have any it does not have any standard deviation therefore the sharpie ratio of risky portfolio quantify we're going to kind of quantify the incremental reward the additional reward okay the additional reward for each increase in one percent of the standard portfolio deviation well in other words as we increase the standard deviation how much are we getting in reward I mean the best way to to kind of explain this let me just show you kind of let me just kind of look at certain graphs and just kind of ask you a few questions and hopefully the sharpie ratio will make will make will make more sense this is earning 10 percent and we have this is stock a and this is stock b stock b is also earning 20 percent and this is the deviation those are the deviation here that goes up it goes down there is the deviation if you choose between a and b which which stock would you take definitely will take b why because the risk notice it's almost the same the deviation is the same it goes up and down but the return is higher so guess what I am I am making more return with less risk I'm earning 20 percent and basically those two are the same risk let me show you another let's assume a and b let's assume this is stock a will earn 10 percent this is stock a and this is let me do a different color stock b and let's look at stock b stock b also earns 10 percent if you are presented with those two stocks which stock would you prefer well I'll prefer stock a why because with the same level with less risk I'm earning 10 percent notice stock b the red one has more risk that does that make sense so you don't want stock you don't want stock b because stock b is riskier stock b has more risk and what am I being compensated I'm not being compensated I'm I'm making 10 percent at the end so I may end up with you know maybe five percent I don't know or I may end up with 20 percent but I am taking risk I don't want to I don't want to take that risk if I can make 10 percent with no risk it's better okay let's look at a third third scenario just to kind of show you what this sharp ratio trying to measure let's assume I can make 10 percent with this let me just a little bit of a little bit of fluctuation 10 percent with this stocks or I can make 11 percent with another stock so this is so this is stock a this is stock b now you need to ask yourself I have an additional 1 percent is it worth taking this is it worth taking all this risk for the additional 1 percent so this is what the sharp ratio trying to measure the relationship between your risk premium your portfolio of risk premium to your standard deviation and what do I mean by standard deviation the standard deviation is the fluctuation is the fluctuation in the stock okay so let's take a look at an example the sharp ratio of a portfolio with an annual risk premium of 8 percent and a standard deviation of 20 so in the numerator we're going to have the 8 percent 0.08 and and standard deviation of 0.2 20 percent will give us a sharp ratio of 0.4 or 40 percent what does that mean a higher sharp ratio indicate a better reward per unit of standard deviation of course it does let me show you was let me show you why so we have 0.08 divided by 20 gave us 0.4 let's assume I want I want if I want to get to a higher ratio if I'm making 10 percent you making the same using the same standard deviation the same risk 0.2 my ratio equal to 0.5 so 0.5 I'm making more return given the same risk of 20 percent so this is what the sharp ratio will measure for us so it's it's very similar to the risk aversion very similar but it just kind of basically looking at something else so the standard deviation I just want to make sure you are aware of this is useful risk measure for diversified portfolio it's not for individual securities when we compute the standard deviation it's for the portfolio and the sharp ratio is a valid statistic for ranking portfolios in terms of in terms of risk premium and standard deviation it's not appropriate to to use it to look at individual assets just want to make sure you understand the the limitation of those in the next session what I would do I would work an example illustrating how to compute the risk aversion and sharp ratio hand in hand because it's very important after you learn the concept to kind of practice an exercise to see how this work as always I'm going to ask you to like and share this recording if you like it and don't forget to visit my website farhatlectures.com to look at additional resources for this course as well as your other resources as well as your other courses or if you're studying for CPA, CFA or CMA exam good luck study hard and stay safe