Slide #1: Lecture 11 – CAPM and SML I: Diversification Principle
Welcome to Lecture 11, which is the first in a series of three lectures on the Capital
Asset Pricing Model and the Security Market Line. In this lecture, we will be discussing
the diversification principle.
Slide #2: Topics covered
We will be covering the following 7 topics in this lecture:
First, we will define and discuss unsystematic risk, systematic risk, and total risk.
Second, we will discuss the measurement of systematic risk and total risk.
Third, having gained an understanding of systematic and unsystematic risk, we will then
discuss the diversification principle.
Fourth, we then use the diversification principle to formulate an equation for calculating
portfolio risk.
We then move on to a numerical example in which we calculate the risk on a portfolio.
We end the lecture, as always, with a practice question, plus check answers, of course.
Slide #3: Unsystematic risk
What is unsystematic risk? Unsystematic risk is any risk that is specific to one firm or
one group of firms (say, an industry or a group of competing firms). This is why
unsystematic risk is also sometimes called unique risk (as in, risk unique to a firm or a
group of firms), and also, asset-specific risk (as in, risk specific to an asset or a group of
assets). An example of unsystematic risk is the risk that changes in wheat prices will
affect wheat producers but not oil producers. That is, the risk of wheat prices dropping
will uniquely or specifically affect wheat producers.
Unsystematic risk is also called diversifiable risk because it can be diversified away by
the simple act of adding more assets to the portfolio. Since unsystematic risk is unique
to an asset or group of assets, when we have a lot of different assets in a portfolio, and
one group of assets is adversely affected (i.e., their share prices go down), it is likely
that other assets in the portfolio will be positively affected (i.e., their share prices go
up). As a result, the overall effect on the portfolio will turn out to be minimal, as the
“up” prices balance out the “down” prices.
For example, let’s say that we have shares in both gold mining companies and financial
companies (such as banks), and the two have historically had returns that are inversely
related to each other. Then a rise in the financial stock prices will be accompanied by a
fall in the gold stock prices, and vice versa. Therefore, the overall impact on the
portfolio return is minimal.
Slide #4: Systematic risk
Systematic risk is risk that affects many or all assets in an economy. An example of a
systematic risk is the risk of economic upheaval, such as the financial crisis in 2007.
This risk affects all companies globally. That is why systematic risk is also called market
risk or non-diversifiable risk. This risk is not diversifiable because adding more assets to
the portfolio will not absolve the portfolio from the effects of risk that covers all assets in
the economy or in the portfolio.
Slide #5: Total risk
So, now we come to total risk. For each asset or each portfolio, the total risk is
comprised of unsystematic risk and systematic risk:
Total risk = Systematic risk + Unsystematic risk,
where systematic risk is measured by a thing called beta, and total risk is measured by
the standard deviation of returns on the asset or portfolio.
The term beta will be discussed in more depth in another lecture. At this point, all you
need to know is that beta measures the level of systematic risk on an asset or portfolio.
Ironically, there is no unique measure of the unsystematic risk on the asset or portfolio.
Slide #6: Risk Comparison example
The concepts of total and systematic risk measures are very useful when we want to
compare the risk levels of different assets. Let’s look at these two stocks here:
How do they compare in terms of their total risk, systematic risk, and unsystematic risk?
Since Stock A has a higher standard deviation than Stock B, we know that Stock A has
the higher total risk.
On the other hand, since the beta on Stock B is higher than the beta on Stock A, we
know that Stock B has a higher systematic risk than Stock A. What this means is that
Stock B is more affected by changes in the overall economy than Stock A.
Now, what about unsystematic risk? Which stock has the higher unsystematic risk? We
know that
Total risk = Systematic risk + Unsystematic risk.
This means that we can rewrite the formula to give us:
Unsystematic risk = Total risk – Systematic risk.
Since Stock A has high Total risk but low systematic risk, this means that Stock A also
has high unsystematic risk.
Slide #7: Diversification principle
And now, we come to the diversification principle: The diversification principle tells us
that, as we add more and more different assets into our portfolio, we will be able to
diversify away the unsystematic risk of the specific assets, but not the systematic risk.
Therefore, at some point in adding assets to our portfolio, we will be able to eliminate
the unsystematic risk of specific assets, and what is left in the portfolio will only be
systematic risk, as depicted in the figure below:
Unsystematic risk
Unsystematic risk
As we add more and more stocks into our pot, the unsystematic risks are taken out of
the pot, and only the systematic risk is funneled through. The resulting portfolio risk will
then only consist of systematic risk from our assets.
In fact, when we test this principle empirically, we have found the portfolio risk stabilizes
to an almost constant level after adding only 30 assets (shares) into our portfolio. You
can check this easily by finding 30 different shares from various industries, form a
portfolio, and track the portfolio risk through time. As you add more assets to the
portfolio, you will find that the portfolio risk will level out.
Slide #8: Portfolio risk
The diversification principle is very important because it allows us to calculate the beta
on a portfolio as the weighted sum of the betas on individual assets in the portfolio.
That is, the portfolio risk is only dependent on the beta (read systematic risk) on
individual asset and not on their total risk (standard deviation) because, of course, in a
diversified portfolio, the asset-specific risk has been diversified away according to the
diversification principle.
Slide #9: Numerical Example
Now, let’s work through an example of calculating portfolio risk. Say we have a portfolio
that invests equally in 3 mutual funds. The expected returns and betas are provided in
the table below. What is the portfolio beta?
Aggressive Fund (A)
Fundamentals
(F)
Passive
(P)
Expected Return
30%
15%
5%
Beta
2.5
1.2
0.7
We have the betas for the mutual funds:
βA = 2.5
βF = 1.2
βP = 0.7
Slide #10: Numerical example (cont.)
The portfolio beta is equal to the weighted sum of the individual betas. In this case,
since the portfolio is equally invested in the three mutual funds, the portfolio weight on
each is one-third:
wA = wB = wC = 1/3
Note that the sum of the portfolio weights must always be equal to 1:
wA + wB + wC = 1/3 + 1/3 + 1/3 = 1
The portfolio risk, or portfolio beta is calculated with the following formula:
Portfolio Risk
= p
= wAA + wBB + wCC
Plugging in the values for portfolio weights and betas, we calculate the portfolio risk as
p = (1/3)(2.5) + (1/3)(1.2) + (1/3)(0.7)
= 0.833333 + 0.4 + 0.233333
= 1.466667
Slide #11: Practice problem
And a long time ago, in a galaxy far, far away … There was practice!
question for you. Try to see if you can solve this problem:
So here’s a
You have a portfolio made up of a market index and an equity index. The portfolio beta
is 1.6, and the beta on the market index is 1. If you are 40% invested in the market
index, what is the beta on the equity index?
Slide #12: Check answers to practice problem
Here are your check answers. Have fun!
p = 1.6
1 = 1
w1 = 0.4
w2 = 1 – 0.4 = 0.6
p = w11 + w2 2
1.6 = 0.4(1) + 0.62
1.6 – 0.4 = 0.6 2
2 = 1.2 / 0.6 = 2
Slide #13: End of Lecture 11
Here ends Lecture 11 on the diversification principle.