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FINS1613 BUSINESS FINANCE
TUTORIAL WEEK 9
(Based on Lecture 8, RTBWJ Chapter 11)
[1] Read and ponder on possible solutions to questions under CRITICAL THINKING AND CONCEPTS
REVIEW
11.1, 11.3, 11.5, 11.7, 11.8
1.
Some of the risk in holding any asset is unique to the asset in question. By investing in a variety
of assets, this unsystematic portion of the total risk can be eliminated at little cost. On the other hand,
there are systematic risks that affect all investments. This portion of the total risk of an asset cannot be
costlessly eliminated. In other words, systematic risk can be controlled, but only by a costly reduction in
expected returns.
3.
a.
systematic
b.
unsystematic
c.
both; probably mostly systematic
d.
unsystematic
e.
unsystematic
f.
systematic
5.
No to both questions. The portfolio expected return is a weighted average of the asset returns,
so it must be less than the largest asset return and greater than the smallest asset return.
7.
Yes, the standard deviation can be less than that of every asset in the portfolio. However,
portfolio beta cannot be less than the smallest beta because it is a weighted average of the individual
asset betas.
8.
Yes. It is possible, in theory, to construct a zero beta portfolio of risky assets whose return would
be equal to the risk
‐
free rate. It is also possible to have a negative beta; the return would be less than
the risk
‐
free rate. A negative beta asset would carry a negative risk premium because of its value as a
diversification instrument.
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[2] Solve these problems from Chapter 11 under QUESTIONS AND PROBLEM
Q10, Q12, Q19, Q22, Q33
10.
a.
This portfolio does not have an equal weight in each asset. We first need to find the return of
the portfolio in each state of the economy. To do this, we will multiply the return of each asset
by its portfolio weight and then sum the products to get the portfolio return in each state of
the economy. Doing so, we get:
Boom:
E(R
p
) = .30(.30) + .40(.45) + .30(.33)
E(R
p
) = .3690 or 36.90%
Good:
E(R
p
) = .30(.12) + .40(.10) + .30(.15)
E(R
p
) = .1210 or 12.10%
Poor:
E(R
p
) = .30(.01) + .40(–.15) + .30(–.05)
E(R
p
) = –.0720 or –7.20%
Bust:
E(R
p
) = .30(–.20) + .40(–.30) + .30(–.09)
E(R
p
) = –.2070 or –20.70%
And the expected return of the portfolio is:
E(R
p
) = .15(.3690) + .45(.1210) + .35(–.0720) + .05(–.2070)
E(R
p
) = .0743 or 7.43%
b.
To calculate the standard deviation, we first need to calculate the variance. To find the
variance, we find the squared deviations from the expected return. We then multiply each
possible squared deviation by its probability, and then sum. The result is the variance. So, the
variance and standard deviation of the portfolio is:
p
2
= .15(.3690 – .0743)
2
+ .45(.1210 – .0743)
2
+ .35(–.0720 – .0743)
2
+ .05(–.2070 – .0743)
2
p
2
= .02546
p
= (.02546)
1/2
P
= .1596 or 15.96%
12.
The beta of a portfolio is the sum of the weight of each asset times the beta of each asset. If the
portfolio is as risky as the market, it must have the same beta as the market. Since the beta of the
market is one, we know the beta of our portfolio is one. We also need to remember that the beta
of the risk
‐
free asset is zero. It has to be zero since the asset has no risk. Setting up the equation for
the beta of our portfolio, we get:
p
= 1.0 =
1
/
3
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 Standard Deviation, Variance, Errors and residuals in statistics, Stock B, Boom

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