[MUSIC] Last time we talked about the relationship between risk and return. In this video, we will talk about diversification and the two types of risks, mainly diversifiable and systematic risk, and whether both risks affect returns or not. Let's think about the risk of a company's stock. If the company succeeds, then the shareholders make a lot of money. On the other hand, if it fails, stockholders lose their money. If an investor puts all her wealth in one stock and that company fails, then she loses all her wealth. This makes investments in only one stock extremely risky. It is better to invest in more than one stock, as it helps spread the risk. Note, a combination or collection of stocks is referred to as a portfolio. In a portfolio, there may be some stocks that perform badly, but there are likely other stocks that offset at least part of this bad performance. Conversely, the good performance of some stocks may be offset by the bad performance of other stocks in the portfolio. This tells us that the risk or uncertainty of a portfolio is likely to be far lower than the risk of a single stock. This is the idea of diversification. The figure that you see plots portfolio variance on the vertical axis against the number of stocks in the portfolio on the horizontal axis. Here, portfolio variance is a measure of a risk. The blue curve captures the relationship between risk and the number of stocks in the portfolio. And represents the total variance or risk of the portfolio. As you can see, increasing the number of stocks in the portfolio reduces its variance. This drop in risk with increasing number of stocks in the portfolio captures the idea of diversification. The part of risk that is eliminated by forming a large enough portfolio is called diversifiable risk. In the figure, it is the gap between the blue curve and the horizontal black line. This gap becomes negligible by the time there are 50 to 60 stocks in the portfolio. However, beyond 50 to 60 stocks in the portfolio, its risk cannot be reduced any further. That is, we cannot achieve any further diversification. The part of risk that cannot be eliminated any further with the addition of more stocks is referred to as systematic risk. In the figure, it is the gap between the horizontal black line and the horizontal axis. If forming sufficiently large portfolios can eliminate diversifiable risk, investors should not expect to be compensated for holding diversifiable risks. Let's look at a simple example to illustrate this. Say there are four stocks A, B, C, and D and there is a risk-free bond. The risk-free rate is 5% per year. Stock A is expected to give a return of 12% over the next one year. Similarly stocks B,C, and D are expected to give returns of 15, 17, and 20% respectively over the next one year. Further, let's assume that none of the four stocks have any systematic risk. This means that A's additional 7% return over and above the risk-free rate is compensation only for its diversifiable risk. The same can be said about the other three stocks, that is, all four stocks compensate investors for holding only diversifiable risk. Given that D offers the largest compensation above the risk-free rate and A the least, D has the largest amount of diversifiable risk and A has the least. Now let's form a portfolio with $100 and put $25 in each of the four stocks. So 25% of our wealth is in each of these stocks. Let's assume that the resultant portfolio has no diversifiable risk. In other words, they're able to completely diversify away a risk by forming this portfolio. For instance, none of the stocks had any systematic risk to begin with, this portfolio will also have no systematic risk. Consequently, this portfolio has absolutely no risk, that is, it is a risk-free portfolio. This means that it should also have a 5% expected return, the same as a risk-free bond. The expected return of a portfolio is a weighted average of the individual stock's expected return. Here, it is 0.25 x 12% +0.25 x 15% + 0.25 x 17% + 0.25 x 20%. Which works out to 16% per year. Clearly something is not right. The portfolio has zero risk but has a return of 16%, which is much higher than the risk-free rate of return of 5%. This gives rise to what is called to an arbitrage opportunity, that is the ability to make guaranteed profits with no risk. Investors will borrow at the risk-free rate of 5% and invest in this portfolio and earn a guaranteed 16%. The buying of these stocks will put an upward pressure on the prices of the four stocks, consequently reducing their returns. This will happen until all stocks are expected to give a return of 5%. So investors expecting to be compensated for holding diversifiable risk is not sustainable in the long run. Hence, they will be compensated only for systematic risk, that is, risk that is not diversifiable. Now that we have a better understanding of the discount rate and the key factor that drives it, namely systematic risk. Next time we will start talking about the various investment decision tools that a manager may use to decide on which projects to invest in. [MUSIC]
