TERM STRUCTURE OF INTEREST RATES
There is no single market yield
 Every bond has its own yield
Bond Yields
All bond yields can be expressed as:
Bond Yield=Base Rate+ Spread


The base rate (the benchmark rate)
o Base Rate: the minimum interest rate inv
premium estimates can range from equity premium tends to be large
and this can make a big difference. about 1% per year to about 8% per
yeara large range. To date, there is no universally accepted method to
estimate the expected rate of return on the mark
worked this out for you. In our example, the minimumvariance portfolio
has a weight of 76.191% on H and 23.809% on I, and it achieves 8.8
GRAPHING THE MEANVARIANCE EFFICIENT FRONTIER 237
Standard deviation of rate of return (risk) Expected rate of return
are higher than Geometric versus arithmetic geometric rates of return.
(A +20% rate of return followed by a 20% rate of return averages,
Section 7.1A, p. 180 gives you a 0% arithmetic average, but leaves you
with a 2year loss of 4%.) Thus, if your projec
short rate, because shortterm bonds are typically safer and therefore
closer to the riskfree asset that is in the spirit of the CAPM. This is why
you may want to add another 1% to the equity premium estimates
calculated in this tablethe longterm govern
covariance term. It also means that we can compute the standard
deviation more easily: Sdv(rS) = (1/2)2 . 90% = 1/2 . 90% 1/2 .
9.49% 4.74% Sdv(rS) = (wH)2 . Var(rH) = wH . Var(rH) = wH .
Sdv(rH) (8.14) This states that the risk of your overall portfolio
equity premiums. The equity premium estimation is usually done in two
steps: First, you must estimate a statistical regression that predicts next
years equity premium with this years dividend yield; then, you
substitute the currently prevailing dividend y
high past equity returns could have been not just due to high exante
equity premiums, but due to historical bubbles in the stock market. The
proponents of the bubble view usually cannot quantify the appropriate
equity premium, but they do argue that it i
(20%) 2 + (20%) 2 = 2 . (20%) 2 = 800% Therefore, the standard
deviation is 2 . 20% 28%. (e) The Sharpe ratio is 2 . (12%
6%)/28% 0.43. (f) The variance is 4 . (20%)2 = 1600%. The
standard deviation is 20% . 4 = 40%. The Sharpe ratio is (6% . 4)/(20%
. 4
between 2% and 4%. (Incidentally, it is my impression that there is
relatively less disagreement about equity premium forecasts today than
there was just 5 to 10 years ago.) But realize that reasonable individuals
can choose equity premium estimates as lo
about 24.8% in I. (Work with the rounded numbers to make your life
easier.) With the riskfree asset offering 4%, what portfolio would you
purchase that has the same risk, and what would its improvement in
reward be? First think about how to solve this. H
Var(rP) = Var[wH . rH + (1 wH) . rI] (8.12) If there are assets that
can be combined to construct a riskfree asset, then the minimumvariance portfolio will touch the yaxis at 0. If there are only two assets,
this means their correlation would have to be
rates of return. But it is not even clear whether the higher returns for
value firms reflect appropriate rewards for risktaking that investors
require (and which therefore should flow into a hurdle rate), or whether
these firms earned superior returns be
risk of new corporate investment projects, then you can determine their
appropriate costs of capital in the NPV formula. Alas, like NPV, the
formula may be simple, but the application is hard. The devil is in the
details. We will first review what you alr
of risky assets. of the riskfree asset and whatever portfolio on the
previous efficient frontier would be tangentyou tilt the line up until it
just touches the meanvariance frontier among the risky assets. This line
is called the capital market line. He
probability. The riskfree rate is 3% per annum, and the equity premium
is 5% per annum. (a) What is the price of this bond? (b) What is its
promised rate of return? (c) Decompose the bonds quoted rate of return
into its components. Q 9.10 Going to your s
70 the NPV formula. The basic conclusion was that for shortterm
projects, getting the cash flows right is more important than getting the
expected rates of return right; for longterm projects, getting both right is
important. We just discussed the relat
beyond what riskfree projects are offering. Worse: Not only is the
equity premium difficult to estimate, but the value you choose can also
have a tremendous influence over your estimated cost of capital. Of
course, the theoretical CAPM model assumes that
asset. Therefore, it is also meanvariance efficient. IMPORTANT: In the
CAPM, the market portfolio of risky claims is the tangency portfolio.
(Of course, conversely, if some investors do not hold the market
tangency portfolio, then the overall market port
PRICING MODEL (c) The riskfree rate is 3%, so this is the time
premium (which contains any inflation premium). The (expected) risk
premium is 1%. The remaining 1.05% is the default premium. Q 9.10
The cost needs to be discounted with the current interest
the xaxis and the portfolio reward on the yaxis between risk and
reward. for each portfolio from Table 8.4 on page 232. Figure 8.5 does
it for you. Can you see a pattern? To make it easier, I have taken the
liberty of adding a few more portfolios. (You
stock market overall. For example, in a CAPM world with a riskfree
rate of 3% and an equity premium of 5%, a stock with a market beta of
zero would be expected to earn about 3% on average, regardless whether
the stock market went up or down by 20% this m
INVESTMENT PROJECTS MARKET BETAS Unlike the riskfree
rate and Finally, you must estimate your projects market beta. It
measures how the rate of the equity premium, beta is specific to each
project. return of your project fluctuates with that of the overa
infuse a bit more of my personal opinion now. Different academics draw
the CAPM with caution in a corporate finance context for capital
budgeting. different conclusions from the empirical evidence. Some
recommend outright against using the CAPM, but most
for combination portfolios of a riskfree asset F with any risky portfolio
P, they lie on the straight line between F and P. But would you really
want to purchase such a combination of H and F? Could you purchase a
different portfolio in combination with
90% + (1/3)2 . 189% + 2 . (2/3) . (1/3) . 45% = 81%. Q 8.34 The
covariance between H and I is 45% (Formula 8.9). The variance of H
is 90%, the variance of I is 189% (Table 8.4). Therefore, the shortcut
Formula 8.10 gives Var(rM) = (3/4) 2 . 90% + (1/4) 2
Sdv(rP) = w2 H . Var(rH) + w2 I . Var(rI) + 2 . wH . wI . Cov(rI,
rH) (If you wish, you can first confirm this: This portfolio would return
12.6% (), 18.6% (), 26.4% (), or 4.8% (). Therefore, the expected
rate of return is 9.3%, and the standard deviatio