Risk, Return, and the Historical Record

Question 1

No matter how long the historical record, there is never a guarantee that it exhibits the worst (or best) that nature might
throw at us in the future.

Answer 1

The black swan problem.

Question 2

defined as the percentage increase in funds per year.

Answer 2

effective annual rate (EAR)

Effective annual rates explicitly account for compound interest.
In contrast, rates on short-term investments (by convention, with holding periods less than a year), are in practice often annualized using simple interest that ignores compounding.

Question 3

reflects the true cost of borrowing or the true yield on an investment in terms of purchasing power.

Answer 3

The real rate of interest.

rreal≈rnom−i

Question 4

Define nominal interest rate.

Answer 4

This is the rate at which the dollar value of your
account grows.

So not adjusted for inflation.

Question 5

If the nominal interest rate on a 1-year CD is 8%, and you expect inflation to be 5% over the coming year, then using the approximation formula, you expect the real rate of interest

Answer 5

to be rreal = 8% − 5% = 3%.
Using the exact formula, the real rate is rreal =

.08− .05
________
1 + .05 = .0286, or 2.86%.

Question 6

determine the real interest rate.

Answer 6

Supply, demand and government action.

Question 7

is the real rate plus the expected rate of inflation.

Answer 7

The nominal interest rate

Question 8

Suppose the real interest rate is 3% per year and the expected inflation rate is 8%. According to the Fisher hypothesis, what is the nominal interest rate?

Answer 8

11%

Expected inflation rate.（8%）+ Real interest rate（3%）

Question 9

is a measure published by the U.S. Bureau of Labor Statistics (BLS) that tracks the average change over time in the prices paid by urban consumers for a market basket of consumer goods and services. This index is widely used to gauge inflation.

Answer 9

Consumer Price Index (CPI) report.

Question 10

the inflation rate comes from the

Answer 10

Consumer Price Index (CPI) report.

Question 11

dividend yield plus the rate of capital gains equals

Answer 11

Holding period return.

Question 12

But what do we mean by an outcome “far” from the mean? A return 15% below the mean would hardly be noteworthy if typical volatility were high—for example, if the standard deviation of returns were 20%—but that same outcome would be highly unusual if the standard deviation were only 5%. For this reason, it is often useful to think about deviations from the mean in terms of how many standard deviations they represent. If the standard deviation is 20%, that 15% negative surprise would be only three-fourths of a standard deviation, unfortunate perhaps, but not uncommon. But if the standard deviation were only 5%, a 15% deviation would be a “three-sigma event,” and quite rare.

Question 13

the risk of outcomes in the far tails of the probability
distribution.

Answer 13

Tail risk.

Longer tails occur when the center becomes slimmer, therefore tighter, increasing the probability of larger standard deviations, hence the term tails.

This, in turn, infers higher degree of risk.

Question 14

concerns the likelihood of extreme values on either side of the mean at the expense of a smaller likelihood of moderate deviations.

Answer 14

Kurtosis.