BFC5935 - Tutorial 3 Solutions PDF
BFC5935 - Tutorial 3 Solutions PDF
BFC5935 - Tutorial 3 Solutions PDF
[Readings: Ch7]
Q1 The capital asset pricing model (CAPM) contends that there is systematic
and unsystematic risk for an individual security. Which is the relevant risk
variable and why is it relevant? Why is the other risk variable not relevant?
In a capital asset pricing model (CAPM) world the relevant risk variable is the
security’s systematic risk - its covariance of return with all other risky assets in the
market. This risk cannot be eliminated. The unsystematic risk is not relevant because
it can be eliminated through diversification - for instance, when you hold a large
number of securities, the poor management capability, etc., of some companies will
be offset by the above average capability of others.
Q2 What are the similarities and differences between the CML and SML as
models of the risk-return trade-off?
Similarities: they both measure the relationship between risk and expected
return.
Differences: First, the CML measures risk by the standard deviation (i.e., total risk)
of the investment while the SML explicitly considers only the systematic
component of an investment’s volatility. Second, as a consequence of the first
point, the CML can only be applied to portfolio holdings that are already fully
diversified, whereas the SML can be applied to any individual asset or collection
of assets.
On the CML the lowest risk portfolio is 100 percent invested in the risk-free asset
with a standard deviation of zero. The SML—focusing on the word “security” in its
name—deals primarily with security or asset risk. Security risk is measured by the
asset’s systematic risk, or beta. Beta can be negative (if the asset’s returns and
market returns are negatively correlated) so the SML extends to the left of the
vertical (expected return) axis.
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Q3 Draw an ideal SML. Based on the early empirical results, what did the actual
risk-return relationship look like relative to the ideal relationship implied by
the CAPM?
Empirical SML
RM
RFR
In the empirical line, low risk securities did better than expected, while high risk
securities did not do as well as predicted.
Q4 According to the CAPM, what assets are included in the market portfolio, and
what are the relative weightings? In empirical studies of the CAPM, what are the
typical proxies used for the market portfolio? Assuming that the empirical
proxy for the market portfolio is not a good proxy, what factors related to the
CAPM will be affected?
The “market” portfolio contains all risky assets available. If a risky asset, be it an
obscure bond or rare stamp, was not included in the market portfolio, then there
would be no demand for this asset and, consequently, its price would fall. Notably,
the price decline would continue to the point where the return would make the
asset desirable such that it would be part of the “market” portfolio. The weights
for all risky assets are equal to their relative market value. The typical proxy for
the market portfolio are stock market indexes.
According to Roll, a mistakenly specified proxy for the market portfolio can have
two effects. First, the beta computed for alternative portfolios would be wrong
because the market portfolio is inappropriate. Second, the SML derived would be
wrong because it goes from the RFR through the improperly specified market
portfolio. In general, when comparing the performance of a portfolio manager to
the “benchmark” portfolio, these errors will tend to overestimate the
performance of portfolio managers because the proxy market portfolio employed
is probably not as efficient as the true market portfolio, so the slope of the SML
will be underestimated.
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Q5
a. You expect an RFR of 10 percent and the market return (RM) of 14 percent.
Compute the expected return for the following stocks, and plot them on an
SML graph.
U 0.85
N 1.25
D −0.20
b. You ask a stockbroker what the firm’s research department expects for
these three stocks. The broker responds with the following information:
U 22 24 0.75
N 48 51 2.00
D 37 40 1.25
Plot your estimated returns on the graph from Part a, and indicate what
actions you would take with regard to these stocks. Explain your decisions.
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Current Expecte Expected
Stock Price d Price Dividend Estimated Return
U 22 24 0.75
24 22 0.75
.1250
22
N 48 51 2.00
51 48 2.00
.1042
48
D 37 40 1.25 40 37 1.25
.1149
37
E(R)
N
14% U
*U’
*D’ * N’
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Q6
a. Explain what the CAPM and APT attempt to model. What are the main
differences between these two asset pricing models?
The Capital Asset pricing Model (CAPM) is an equilibrium asset pricing theory
showing that equilibrium rates of expected return on all risky assets are a function
of their covariance with the market portfolio. The CAPM is a single-index model
that defines systematic risk in relation to a broad-based market portfolio (i.e., the
market index). This single factor (“beta”) is unchanging:
Rj = Rf + Bj(Rm – Rf)
where
(1) Inflation;
(2) Industrial production;
(3) Risk premia as measured by the spread between low and high grade bonds;
(4) Yield curve, (i.e., slope of the term structure of interest rates.
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b. Under what circumstances would the APT be preferred over the CAPM as a
tool for selecting stocks for the fund portfolio?
Because of APT’s more general formulation, it is more robust and intuitively appealing
than the CAPM. Many factors, not just the market portfolio, may explain asset returns.
This permits the stock selection process to take into account as many economic variables
as are believed to be significant in a valuation context – not only as to individual issues,
but also as to groups, sectors or even the market as a whole. For example, given a forecast
of a sudden spurt in the inflation rate, and of the resulting effect on interest rates, the
analyst or portfolio manager can, via APT, arrive at an estimate of valuation changes
across his/her selection universe and adjust portfolio exposures accordingly.
Alternatively, stocks could be selected and portfolios formed based on specific factor-
sensitivity criteria set up in advance.
Q7 Some studies related to the efficient market hypothesis generated results that
implied additional factors beyond beta should be considered to estimate
expected returns. What are these other variables and why should they be
considered?
Empirical studies of the efficient markets hypothesis (EMH) have documented a number
of market anomalies. The three main and oldest anomalies include the size effect, the
book-to-market effect and the momentum effect. Therefore, the size / SMB factor which
captures the smallest firms’ return premium, the BTM / HML factor which captures the
highest BTM firms’ return premium, and the momentum / UMD factor which captures the
winner firms’ return premium, should be considered to estimate security expected
returns. These variables have been shown to have predictive ability with respect to
security returns.