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21.d.i Portfolio Choice
In its most simplistic terms, CAPM recognizes that each portfolio will consist of some combination of riskless assets and risky assets and that an investor can choose how much to invest in each of these two types of assets.
Graph 21.d.1 presented above represents a standard view of the options for riskless assets. However, the risk-reward
trade-off curve for only risky assets can be seen below in Figure 21.d.2.
Expected Return
0.25
0.2
0.15
0.1
K
J
I
0.05
H
0
0
0.1
0.2
0.3
0.4
Standard Deviation
Figure 21.d.2. This is a risk-reward trade-off curve for risky assets only. The curve represents
different possible risky asset portfolios. Point I is a minimum-risk point (lowest standard
deviation). Points above this point trade risk for the potential for reward (expected return). Note
that in reality, any risky asset portfolio on the curve that lies below point I will not ever be taken.
The reason is that you are increasing your uncertainty while reducing your expected return, which
is ludicrous.
Now one can combine the two graphs presented above to find the risk-reward combinations that can be
obtained by combining riskless assets with risky assets. Figure 21.d.3 represents all possible combinations for both
risky and riskless asset portfolios. More importantly, it shows that there will be an optimal combination portfolio.
This point lies at the tangency between the two curves.
0.25
Expected Return
0.2
F
0.15
D
0.1
C
J
B
A
0.05
I
E
G
K
H
0
0
0.1
0.2
Standard Deviation
0.3
0.4
Figure 21.d.3. This shows the optimum combination of risky assets and riskless assets. Points D
and J are equivalent and exist as tangency points between the two curves. This is known as the
preferred portfolio for the theoretical relationships between expected return and standard deviation
for risky and riskless assets.
Note that the CAPM does not allow for investors to choose the makeup of the bundle of risky assets that
are held. They can only choose how much of this bundle they will hold relative to their holdings of risk-less assets.
The reason for this is as follows. The CAPM asserts that in equilibrium an investor’s relative holdings of risky
assets will be the same as the market portfolio, which holds all risky assets in proportion to their observed market
values. Its composition is based upon the supply of existing assets, whose relative worth are assessed at current
market prices. This bundle of risky assets – the market portfolio (a risky asset portfolio) – is then the most efficient
bundle and therefore offers the highest possible expected rate of return at a specified level of risk. This is visualized
on a graph just as the point D/J on graph 21.d.3, only one does not have to choose that bundle of risky assets
corresponding to a tangency on the riskless asset line (straight line) because it is put upon the investor as the only
realistically efficient risky asset bundle.
Based upon the results in figure 21.d.3, the possible preferred portfolios – consisting of some riskless assets
and some amount of the market portfolio bundle, together totaling 100% of investments – lie between points A and
D on what can now be called the Capital Market Line (CML) This is depicted as the green line in figure 21.d.4.
0.25
Expected Return
0.2
F
0.15
D
0.1
C
J
B
A
0.05
I
E
G
K
H
0
0
0.1
0.2
0.3
0.4
Standard Deviation
Figure 21.d.4. Show the possible preferred combination portfolios on the green line up to and
including the market portfolio – point D. Point A is only riskless asset investment. All points
between A and D are some combination of market portfolio holdings and riskless asset holdings.
For example, point B appears on the graph as 33 1/3 % market portfolio and 66 2/3 % riskless
assets (the closer you are to point A the more riskless assets you have).
CML Formula: E(r) = rf +
E (rm )  r f
m

Where rf is the expected return for riskless assets (.04), r m is the expected return for the market
portfolio (.1), and σm is the expected standard deviation of the market portfolio. E(r) and σ are the
expected rates of return and standard deviation for the preferred portfolio. Again, consisting of
both the market portfolio of risky assets and the riskless assets.
The following is a graphical explanation of why the market portfolio is the best choice as the risky asset
component of the total preferred portfolio. It is depicted in figure 21.d.5 on the next page.
σ of portfolio return
total risk
nonsystematic
risk
σm
systematic
risk
# of security holdings
Figure 21.d.5. Total risk is composed of both nonsystematic risk (blue line) and systematic risk
(orange line). σm is the standard deviation of the market.
You can see that as one increases their security holdings, thus approaching the market portfolio (increase
number of security holdings), they will rid themselves of all nonsystematic risk – security specific risk. Since
systematic risk – market risk – is always there, you cannot get rid of it. So the goal is to minimize as much risk as
possible, and that only includes nonsystematic risk. This is called diversification and is one of the principles of the
CAPM, which is why it assumes that all investors will choose the market portfolio for their risky asset component.
We have now established how to choose a preferred portfolio, which will be unique to each investors risk tolerance,
temporal position, etc. However, every preferred portfolio will consist of some combination of not only riskless
asset, but also risky asset – form the market portfolio.
Some Problems:
1. According to the CAPM, a simple method for an investor to create his or her optimal portfolio (what I
have been calling preferred) is to:
a.) invest in riskless asset
b.) invest in self-selected risky assets as well as riskless asset
c.) invest in only self-selected risky assets
d.) invest in some combination of the market portfolio with risk0free asset
2. An investor has a risk aversion equal to the average investor in the market. Market investors hold Honda and
Pepsi stock in the proportion of 1:3. If the above investor has $100,000 to spend on a portfolio, how much will he
spend for Pepsi and Honda stock, respectively?
a.) $10,000/$90,000
b.) $25,000/$75,000
c.) $75,000/$25,000
d.) none of the above
3. Given the following: expected rate of return on riskless assets of .05; expected rate of return on the market of
.15; standard deviation of the market portfolio of .2. What is the CML line and what is the reward to risk ratio?
a.) E(r) = .15 + .5σ; .15
b.) E(r) = .05 + .5σ; .5
c.) E(r) = .15 + .05σ; .05
d.) E(r) = .05 + .5σ; .05
Answers: d, b, b