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Unformatted text preview: Chapter 1 1 Text Questions 3' Problems 19 Some of the risk in holding any asset is unique to the asset in question. By investing in a variety of
assets, this unique portion of the total risk can be eliminated at little cost. On the other hand, there
are some 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. a. systematic b. unsystematic c. both; probably mostly systematic
d. unsystematic e. unsystematic f systematic False. The variance of the individual assets is a measure of the total risk. The variance on a well—
diversiﬁed portfolio is a function of systematic risk only. Yes, the standard deviation can be less than that of every asset in the portfolio. However, [3], cannot
be less than the smallest beta because BP is a weighted average of the individual asset betas. Yes. It is possible, in theory, to construct a zero beta portfolio of risky assets whose return would be
equal to the riskfree rate. It is also possible to have a negative beta; the return would be less than the
riskfree rate. A negative beta asset would carry a negative risk premium because of its value as a
diversiﬁcation instrument. The covariance is a more appropriate measure of a security’s risk in a welldiversiﬁed portfolio
because the covariance reﬂects the effect of the security on the variance of the portfolio. Investors
are concerned with the variance of their portfolios and not the variance of the individual securities.
Since covariance measures the impact of an individual security on the variance of the portfolio,
covariance is the appropriate measure of risk. IS', 8’.qu uamhm. 733 '/ i ‘" @L 5419) = Am 2 .1th + % AOOvugﬂ ._ L. Di: A533 . To ﬁnd the expected return of the portfolio, we need to find the return of the portfolio in each
state of the economy. This portfolio is a Special case since all three assets have the same
weight. To find the expected return in an equally weighted portfolio, we can sum the returns of
each asset and divide by the number of assets, so the expected return of the portfolio in each
state of the economy is: Boom: E(Rp) = (.07 + .15 + .33)/3 = .1833 0 18.33%
Bust: E(R1,) = (.13 + .03 —.06);‘3 = .0333 o 3.33%
To find the expected return of the portfolio, we multiply the return in each state of the economy
by the probability of that state occurring, and then sum. Doing this, we ﬁnd: E(R,) = .80(.1833) + .20(.o333) = .1533 or This portfolio does not have an equal weight in each asset. We still 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,)=.20(.0?) +.20(. 15) + .60(.33) =.2420 or 24.20%
Bust: E02,) =.20(.13) +.20(.03) + .60(—.06) = —.0040 or 4.40% And the expected return of the portfolio is:
E(Rp) : .80(.2420) + .20(—.004) = .1928 or 19.28%
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 add all of these up. The result is the
variance. So, the variance of the portfolio is: .z a: = .30(.2420 — .1928)2 + .20(—.0040 — .1928)2 = .00968 “x... .a. Again, we have a special case where the portfolio is equally weighted, so we can sum the
returns of each asset and divide by the number of assets. The expected return of the portfolio is: E(R,) = (.103 + .05).!2 = .0765 or 7.65% We need to ﬁnd the portfolio weights that result in a portfolio with a B of 0.50. We know the [3
of the riskfree asset is zero. We also know the weight of the riskfree asset is one minus the
weight of the stock since the portfolio weights must sum to one, or 100 percent. So: [3,, = 0.50 = ws(.92) + (1 — w5)(0) 0.50 = .92W5 + 0 — 0W5 ws = 0.50:192 ws = .5435 And, the weight of the risk—free asset is: wa=1—.5435 = .4565 We need to ﬁnd the portfolio weights that result in a portfolio with an expected return of 9
percent. We also know the weight of the riskfree asset is one minus the weight of the stock
since the portfolio weights must sum to one, or 100 percent. So: HR.) = .09 = .103ws + .05(l — ws) .09 = .103Ws + .05 — .OSWS
W5 2 .754? So, the B of the portfolio will be: (3., = .7547(.92) + (1 — .754?)(0) = 0.694 3
Solving for the B of the portfolio as we did in part a, we ﬁnd: Bl, = 1.84 = ws(.92) + (1 — w5)(0) ws =1.84!.92 = 2 wa = 1 _ 2 = —1 The portfolio is invested 200% in the stock and —100% in the riskfree asset. This represents
borrowing at the riskfree rate to buy more of the stock. ...
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 Spring '11
 Bowen

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