[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.
Ramabhadran ThirumalaiAssistant Professor
