MONEY & BANKING (Eco 340)
Ranjit Dighe
Lecture notes to accompany Cecchetti's Chapter 5 ("Understanding Risk")
Last revised (very slightly) on 3April2007.
In these notes:
I. Introducing risk
II. Measuring risk
III. Sources of risk: idiosyncratic and systematic
IV. Risk and diversification
I. INTRODUCING RISK
Risk is defined as the uncertainty of an asset's
return over a given period. We usually think of risk as involving the
possibility of a loss or a major hardship, like losing money in the
stock market or being stranded on a deserted stretch of
highway with a flat tire. But more generally risk just means
uncertainty, a range of possible outcomes, not all of which are
equally good.
Almost all people are risk averse (they have risk
aversion), in that they hate to lose more than they love to win. A
riskaverse person dislikes being exposed to risk, and will
always refuse an evenmoney bet(such as a coin toss with $20
at stake) to the point of paying to avoid such bets. Buying insurance
is a sign of risk aversion. Someone who is not
riskaverse is either riskneutral (indifferent between taking or not
taking evenmoney bets) or riskloving (will always
accept such bets  e.g., habitual gamblers).
 If returns on two assets are equal, riskaverse people will prefer
the lowerrisk asset
 increase in an asset's risk (relative to other assets)
> decreased demand for that asset,
increased demand for all other assets
II. MEASURING RISK
Conceptually, an asset's risk is the volatility of the asset's return.
We can measure that volatility, or variability, of the asset's
return as the
* variance (average squared deviation from mean return) of the asset's
yearly returns, or as the
* standard deviation (typical deviation from mean, or
average, return; equal to the square root of the
variance).
* An alternative that involves only simple arithmetic is the average
(absolutevalue) deviation from the mean return, which
produces a result not far from the standard deviation. The standard
deviation is the preferred measure, however (one reason
why is that it gives more weight to outliers, or large deviations. If
we're riskaverse, then it makes sense to give extra weight
to outliers.)
Two of the most crucial pieces of information about any financial asset
are its mean return (relates to expected return) and
the standard deviation of its yeartoyear returns.
 If the expected return is just a simple average of past returns,
then it's very easy to compute. Alternatively, one might put a
lot more weight on recent returns, or incorporate other information
into one's expectations. The expected value of an
investment is defined as the probabilityweighted sum of the possible
values of an investment. The expected return
on an investment is the expected value of future payouts, minus what
you
paid for the investment. (To put it in percentage terms, we would
then divide that amount by what you paid for the investment, then take
it to the 1/n power (to get an annualized return), and multiply by
100%.)
Old bonus question, long since answered: Q: Suppose that a slot machine costs $1 to play once, and that the player has a 1 in 5,000 chance of a $1,000 payout, a 1 in 500 chance of a $100 payout, a 1 in 50 chance of a $10 payout, and otherwise nothing. What is the expected payout from playing that slot machine? Show your work. A: Expected payout, or Expected value = (Probability of $1000 payout)*($1,000 payout) + (Probability of $100 payout)*($100 payout) + (Probability of $10 payout)*($10 payout) = (1/5000)*($1000) + (1/500)*($100) + (1/50)*($10) = $0.20 + $0.20 + $0.20 = $0.60. (That's the expected payout. Since it costs $1 to play, your expected return from playing is minus forty cents. 
Ex.: A company's stock has had the following yearly returns over the past five years: 5%, 15%, 10%, 2%, 8%
> Mean return = simple average of those = (5+15+10+2+8)% / 5 = 40% / 5 = 8%
Deviations from mean = difference each year's return and the
mean return (yearly return minus mean return)
= 3%, 7%, 2%, 6%, 0%
(calculated as 5%  8%, 15%  8%, 10%  8%, 2%  8%, 8%  8%)
Absolute deviations from mean = absolute values of deviations
= 3%, 7%, 2%, 6%, 0%
Average absolute deviation = simple average of absolute deviations
= (3+7+2+6+0)% / 5
= 18% / 5
= 3.6%
/\

The standard deviation will be pretty close to this number, and only a
bit more complicated to compute. It's the square root
of the variance, which is the average squared deviation from the mean.
So let's first compute the (population) variance, by
taking the squares of those deviations from the mean (which were 3%,
7%, 2%, 6%, 0%), add them up, and divide by 5
(the number of observations):
Variance
= (9% + 49% + 4% + 36% + 0%) / 5
= 98% / 5
= 19.6%.
Taking the square root of that gives us the standard deviation,
which is
4.4%.
So the standard deviation is very much like the average absolute
deviation, except it tends to be a bit bigger. That first step
of squaring all those deviations means that large deviations become
magnified, and the final step of taking the square root of
the average does not entirely undo that magnification.
 For example, consider two more stocks with an 8% mean return and
yearly returns over a fiveyear period of (a) 4%, 12%,
4%, 12%, 8% and (b) 0%, 16%, 8%, 8%, 8%. The standard deviation is 3.6%
for the first, 5.1% for the second.
{Nice to know: On an Excel spreadsheet, the command for the mean or
average is =AVERAGE(range of cells or numbers),
the command for standard deviation is =STDEV(range...), and the command
for variance is =VAR(range...).}
Another useful measure of risk is value at risk,
which is defined as the worst possible loss over a specific
time horizon at
a given probability. One can look at past returns and outcomes
to form a prediction of how large a loss could occur and
how likely it is to occur.
 Ex.: If you have $10,000 and want to invest it in an index fund of
the stock market over the next year, then you might
want to know your odds of losing half of your investment. If a 50% loss
in a oneyear period has occurred in four of the
past 100 years, then you could say you have a 4% probability of losing
$5,000 (i.e., 50% of $10,000).
 Value at risk is a helpful concept because it explains why
riskaverse (or even riskneutral) people would do things like go
to casinos or play the lottery, where the expected return is negative
and you're likely to lose money. The answer is that such
people tend to budget just a small amount of money for casino gambling
or lottery tickets, so they're not putting a lot at risk.
III. SOURCES OF RISK: IDIOSYNCRATIC AND SYSTEMATIC
Two types of risk:
(1) idiosyncratic (firm or industryspecific,
nonsystematic)  unique to the individual firm or industry; can be
diversified away
 Ex.: Nike stock, Philip Morris (tobacco) stock, New York municipal
bonds
 Studies have shown that to eliminate nearly all of the
companyspecific, or nonsystematic, risk in a stock portfolio, you
need own maybe 3040 stocks. The average mutual fund holds 130.
(2) systematic  cannot be diversified away
 Ex.: stocks have systematic risk, because you can never be certain
what will happen to those companies, and fluctuations
in the current interest rate will raise or lower their resale prices
(PDVs). Longterm bonds have systematic interestrate risk
as well.
 Risk that is unique to a particular class of asset, as opposed to a
particular firm or industry, classifies as systematic risk. You can
diversify by holding assets of many different types (e.g., stocks,
bonds, real estate, cash), but you won't be able to
eliminate the risk from your portfolio entirely.
Asset risk = idiosyncratic risk + systematic risk
In a welldiversified portfolio, there is no idiosyncratic (company
or industryspecific) risk. All of the risk is systematic,
arising from the inherent riskiness of the individual components
(stocks, bonds, etc.) of that portfolio.
The standard measure of systematic risk: beta: measures the
sensitivity of an asset's return to changes in the average
return on the entire market. Beta is a numerical measure (a
regression coefficient, to be precise) of the mutual
relationship between market return and asset's return. If beta is 1,
then an increase in the market return of, say, 10% means
that the asset will typically gain 10% as well (a market index fund has
a beta of 1). If beta is 2, then a 10% increase in the
market return typically means a 20% increase in the asset's return. In
an "up" market, a high beta means a high,
aboveaverage return; but in a "down" market, high betas mean
biggerthanaverage losses. Some assets have
negativebetas, meaning that they do poorly when the market does well
and vice versa. Some examples:
 A stockmarket index fund will have a beta of 1, because it holds
the exact same stocks that go into the market average.
 Technology stocks and other newindustry stocks tend to have betas
> 1.
 Utility stocks and those of longestablished companies tend to have
betas < 1.
 Longterm bonds seem to have a beta close to 0. (Stocks and bonds
are substitutes, but both are affected about the same
by things like changes in market interest rates.)
 Precious metals have a beta of less than 0. Their prices tend to go
up when stock prices are down.
The greater an asset's risk, the greater the return it must offer to
induce people to hold it and hence the greater its risk
premium (the extra return on a risky asset, relative to the return on a
riskfree asset like a Treasury bill). This concept will
be explored more fully when we cover chapter 7 ("The Risk and Term
Structure of Interest Rates").
 Ex.: Rock star David Bowie issued $55 million worth of bonds in
early 1997. His capacity to repay was pretty good,
because he had a large and steady stream of income from royalties,
album sales, etc. It's unclear whether those royalties will
rise or fall in the future, but it's a fairly safe bet that they'll be
enough for him to make his bond payments. Still, it's not a
completely safe bet, so compared with Treasury bonds of the same
maturity length (10 years), the Bowie bonds should pay a
higher interest rate. As indeed they did: the Bowie bonds paid 6.9%
interest, and Treasury bonds at the time paid 6.4%
interest. The difference, 0.5% (i.e., 50 basis points), was the risk
premium on the Bowie bonds.
 Side note: Why did Bowie issue those bonds in the first place?
Don't know. He may have wanted the money to finance
some big new investment project, or, as the book suggests, he might
just have wanted the sure thing of having $55 million
right now instead of waiting for the money to trickle in the form of
royalties and other income. So the book is suggesting
that Bowie himself is riskaverse, because he gets $55 million now and
will pay his bondholders out of that
largebutuncertain stream of future royalty income. If his royalties
are less than expected and he can't make the bond
payments, that's a bigger problem for the bondholders than for him.)
IV. RISK AND DIVERSIFICATION
How can we avoid risk and still earn a decent rate of return? One
popular solution is diversification, ordiversifying your
portfolio. Diversification, in keeping with the old cliche "Don't put
all of your eggs in one basket," is the art of putting your
eggs in several different baskets.
DIVERSIFICATION: holding a variety of (risky) assets
> reduces the overall riskiness of your portfolio. When
one asset tanks, others might not.
 Ex.: Stocks may have the highest rate of return, but, to avoid risk,
you should
(1) hold a variety of stocks (e.g., through a mutual fund);
(2) hold several other assets, too (bonds, moneymarket accounts, ...).
Key point: Diversification reduces the riskiness of your portfolio
even if all of your assets carry equal risk.
 Ex.:
* 2 beer companies: Samuel Adams (highend), Beast (lowend). Both
issue stock.
* 2 states of the economy: good, bad. Each occurs with 50% probability
(or half the time).
* You have $1000 to invest
Samuel Adams does well when the economy is good ("procyclical"),
Beast does well when the economy is bad
("countercyclical"). In the different states of the economy, the
returns on the two stocks are:
State of the economy  Expected Return  
Good  Bad  
Samuel Adams  20%  10%  .5 * 20%
+ .5 * (10%) = 5% 
Beast  10%  20%  .5 * (10%)
+ .5 * (20%) = 5% 
State of the economy  Expected Return  
Good  Bad  
½ Samuel Adams,
½ Beast 
5%*  5%**  5% 
** .5 * (10%) + .5 * (20%) = 5%
 In this example, the returns on Samuel Adams and Beast are perfectly
negatively correlated with each other (when one
goes up 20%, the other one always goes down 10%). In the real world,
there is lessthanperfect, but still some negative
correlation among assets (e.g., gold and real estate perform well when
stocks perform badly), so there is ample scope for
risk reduction by diversification.