[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, namely diversifiable and systematic risk, and also whether both risks affect returns or not. Let's think about the risk of a company's stock. If the company succeeds, then its stock orders 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 the company fails, then she loses all her wealth. This makes investments in only one stock very risky, it is better to invest in more than one stock as this helps spread the risk. Note, a combinational collection of stocks is referred to as a portfolio. In a portfolio, there may be some stocks that perform badly, but there are likely to be others that offset at least part of this bad performance. Conversely, the good performance of some stocks will 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 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 it's 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 horizontal axis. Performance sufficiently large portfolios can eliminate diversifiable risk Investor should not expect to be compensated for holding diversifiable risk. Let's look at a simple example to illustrate this. Say there're four stocks A, B, C and D and 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 1 year. Similarly, stocks B, C and D are expected to give returns of 15, 17 and 20% respectively over the next 1 year. Further, let's assume that none of the four stocks have any systematic risks. This means that A's additional 7% return all about there is free rate, it's compensation only for it's diversifiable risk. The same can be said about the other three stocks. That is, all four stocks compensate investors only for holding diversifiable risk. Given that D offers the largest compensation of risk free rate and A the least, D has the largest amount of diversifiable risk and A has the least amount. Now, let's follow portfolio with $100, and put $25 in each of the 4 stocks. So 25% of our wealth is in each of the stocks. Let's assume that the resultant portfolio has no diversifiable risk. In other words, we are able to completely diversify away our risk by forming this portfolio. Further, since none of the stocks had any systematic risk to begin with, this portfolio also will have no systematic risk. Consequently, this portfolio also has absolutely no risk. That is, it is a risk-free asset. This means that it should also have a 5% expected return, the same as the risk-free asset. The expected $100 for portfolio is a weighted average of the individual stocks and returns. Here it is 0.25 x 12% +0.25 x 15% + 0.25 x 17% + 0.25 x 20% which works out to be 16% per year. Clearly, something is not right. The portfolio has 0 risk, but has a return of 16% which is much higher than the risk free rate. This gives rise to what is called an arbitrage opportunity, that is the ability to make guaranteed profits. Investors will borrow a risk free rate of 15% 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 honor 5% return. 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. Next time we will start talking about how to measure systematic risk and the models that relate measures of systematic risk to expected returns. [MUSIC]
