|
U
, if rain –
) (R, if rain – ) +
Prob. sun (
U
, if sun–
) (R, if sun – ).
From the preceding table of returns and assumed
probabilities, we can fill in the relevant numbers:
COV
UR
= ½ (0.50 – 0.125) (–0.25 – 0.125) + ½ (–0.25 –
0.125) (0.50 – 0.125) = –0.141.
Whenever the returns from two securities move in tandem
(when one goes up, the other always goes up), the covariance
number will be a large positive number. If the returns are
completely out of phase, as in the present example, the two
securities are said to have negative covariance.
*
In general, the beta of a portfolio is simply the weighted
average of the betas of its component parts.
*
Those who remember their high school algebra will recall
that any straight line can be written as an equation. The
equation for the straight line in the diagram is:
Rate of Return = Risk-free Rate + Beta (Return from
Market – Risk-free Rate).
Alternatively, the equation can be written as an expression
for the risk premium, that is, the rate of return on a portfolio
of stocks or any individual stock over and above the risk-free
rate of interest:
Rate of Return – Risk-free Rate = Beta (Return from
Market – Risk-free Rate).
The equation says that the risk premium you get on any
stock or portfolio increases directly with the beta value you
assume. Some readers may wonder what relationship beta has
to the covariance concept that was so critical in our
discussion of portfolio theory. The beta for any security is
essentially the same thing as the covariance between that
security and the market index as measured on the basis of
past experience.
*
Assuming expected market return is 15 percent and risk-free
rate is 10 percent.
*
“Quant” is the Wall Street nickname for the quantitatively
inclined financial analyst who devotes attention largely to the
new investment technology.
*
Final value of investing in all equity funds vs. investing in
only surviving funds.
*
In 2010 anyone, regardless of income, was allowed to
convert a regular IRA into a Roth IRA.
*
Comprehensive information about 529 plans, as well as
other tax-advantaged savings vehicles such as Coverdell
Education
Savings Accounts,
can
be
found
at
www.savingforcollege.com.
*
This isn’t always the case. During some periods, short-term
securities actually yielded more than long-term bonds. The
catch was that investors could not count on continually
reinvesting their short-term funds at such high rates, and later
short-term rates had declined sharply. Thus, investors can
reasonably expect that continual investment in short-term
securities will not produce as high a return as investment in
long-term bonds. In other words, there is a reward for taking
on the risk of owning long-term bonds even if short-term
rates are temporarily above long-term rates.
*
Economists often put the proposition in terms of the risk
premium—that is, the extra return you can expect from an
investment over and above the return from perfectly
predictable short-term investments. According to this view,
the risk premiums in the 1960s were very small, perhaps one
or two percentage points. During the early 1980s, risk
premiums demanded by investors to hold both stocks and
bonds expanded to a range of probably four to six percentage
points, as I shall show below.
*
Technically, the finding that risk is reduced by longer
holding periods depends on the mean-reversion phenomenon
described in chapter 11. The interested reader is referred to
Paul Samuelson’s article “The Judgment of Economic Science
on Rational Portfolio Management” in the
Journal of
Portfolio Management
(Fall 1989).
*
Standard deviation of return.
†
Stocks represented by a Russell 3000 Total Stock Market
Fund. Bonds represented by a Barclays Aggregate Total
Bond Market Fund. (Taxes not considered.)
†
Stocks represented by a Russell 3000 Total Stock Market
Fund. Bonds represented by a Barclays Aggregate Total
Bond Market Fund. (Taxes not considered.)
*
I assume that the savings can be made in an IRA or other
tax-favored savings vehicle, so income taxes on interest
earnings are ignored.
*
In the ninth edition of this book, I recommended a 4½
percent rule because bond yields were considerably higher
than they were in 2010.
*
A short-term bond fund may be substituted for one of the
money-market funds listed.
†
Although it doesn’t fit under the rubric of an index-fund
portfolio, I recommend that investors consider putting part of
the bond portfolio (5 percent of the total portfolio) in
Treasury inflation-protection securities.
*
Some discount brokers offer commission-free trading of
ETFs.
*
Indeed, when you buy a new closed-end fund at par value
plus about 5 percent for underwriting commissions, not only
do you get hit with the equivalent of a large loading fee but
you also run the risk that the fund will sell at a discount at
some time in the future. Never buy a closed-end fund at its
initial offering price. It will almost invariably turn out to be a
bad deal. It may be worth checking, however, to see whether
discounts widen in the future during unsettled market
conditions.
Do'stlaringiz bilan baham: | 
