Risk, Return and The Historical Record

Question 1

What does the economy’s equilibrium level of interest rates depend on?

a) The willingness of households to save, as reflected in the supply curve of funds.
b) The expected profitability of business investment in plant, equipment and inventories, as reflected in the demand curve for funds.
c) The willingness of households to buy commodities, as reflected in the supply curve of funds.
d) The level of inflation
e) Government fiscal and monetary policy.

Answer 1

a) The willingness of households to save, as reflected in the supply curve of funds.
b) The expected profitability of business investment in plant, equipment and inventories, as reflected in the demand curve for funds.
e) Government fiscal and monetary policy.

Question 2

Why is assets with guaranteed nominal interest rate risky in real terms?

a) Because the future inflation is known
b) Because the future inflation is constant as we see today
c) Because the future inflation is uncertain
d) None of the above

Answer 2

c) Because the future inflation is uncertain

Question 3

The equilibrium expected rate of return on any security is the sum of which of the following?

a) The equilibrium real rate of interest
b) The equilibrium nominal rate of interest
c) The expected rate of inflation
d) A market risk premium
e) A security specific risk premium

Answer 3

a) The equilibrium real rate of interest
c) The expected rate of inflation
e) A security specific risk premium

Question 4

Which trade-off does investors face?

a) Between risk and expected return
b) Between risk and expected inflation
c) Between expected return and expected inflation
d) Between risk and equilibrium level of interest rates

Answer 4

a) Between risk and expected return

Historical data confirm our intuition that assets with low degrees of risk should provide lower returns on average than do those of higher risk.

Question 5

Which of the following measures quantify the deviation from normality?

a) Skew
b) Kurtosis
c) VaR
d) LPSD (lower partial SD)
e) Expected shortfall (ES)

Answer 5

a) Skew
b) Kurtosis
d) LPSD (lower partial SD)

Question 6

What does the expected shortfall (ES) measure?

a) The loss that will be exceeded with a specified probability such as 1% or 5%.
b) The expected rate of return conditional on the portfolio falling below a certain value.
c) The ratio of the average cubed deviations from the sample average, called the third moment, to the cubed standard deviation.
d) The expected loss on a short position

Answer 6

b) The expected rate of return conditional on the portfolio falling below a certain value.

Question 7

True or false.

Investment in risky portfolios do become safer in the long run.

Answer 7

False.

Investment in risky portfolios do NOT become safer in the long run.

On the contrary, the longer a risky investment is held, the greater the risk. The basis of the argument that stocks are safe in the long run is the fact that the probability of an investment shortfall becomes smaller. (However, probability if shortfall is a poor measure of the safety of an investment - it ignores the magnitude of possible losses).

Question 8

From what does the discrepancy between geometric and arithmetic average arise?

a) The asymmetric effect of positive and negative rates of returns on the terminal value of the portfolio.
b) The symmetric effect of positive and negative rates of returns on the terminal value of the portfolio.
c) The difference in annual increase in wealth.
d) The difference in annual decrease in wealth.

Answer 8

a) The asymmetric effect of positive and negative rates of returns on the terminal value of the portfolio.

Question 9

When is SD a good measure of risk?

a) When returns are asymmetric
b) When returns are constant
c) When returns are symmetric
d) When returns are equal to 0

Answer 9

c) When returns are symmetric

Question 10

What does the nominal interest rate imply?

a) The growth rate of your purchasing power
b) Your historical purchasing power
c) Your historical growth of your money
d) Growth rate of you money

Answer 10

d) Growth rate of you money

Question 11

What does the real interest rate imply?

a) The growth rate of your purchasing power
b) Your historical purchasing power
c) Your historical growth of your money
d) Growth rate of you money

Answer 11

a) The growth rate of your purchasing power

Question 12

Why does the supply curve of the real interest rate slope up from left to right?

a) Because the higher the real interest rate, the lower the supply of household savings
b) Because more businesses will want to invest in physical capital
c) Because less businesses will want to invest in physical capital
d) Because the higher the real interest rate, the greater the supply of household savings

Answer 12

d) Because the higher the real interest rate, the greater the supply of household savings

Question 13

Why does the demand curve of real interest rates slope down from left to right?

a) Because the higher the real interest rate, the lower the supply of household savings
b) Because more businesses will want to invest in physical capital
c) Because less businesses will want to invest in physical capital
d) Because the higher the real interest rate, the greater the supply of household savings

Answer 13

b) Because more businesses will want to invest in physical capital

Question 14

Which of the following is the Fisher equation?

a) r_nom=r_real+E(i)
b) r_nom=r_real-E(i)
c) r_real=r_nom-E(i)
d) r_real=r_nom+E(i)

Answer 14

a) r_nom=r_real+E(i)

Question 15

What is the excess return?

a) The difference between the expected rate of return on a risky asset and the actual risk-free rate
b) The difference between the actual rate of return on a risky asset and the expected risk-free rate
c) The difference between the actual rate of return on a risky asset and the actual risk-free rate
d) The difference between the expected rate of return on a risky asset and the expected risk-free rate

Answer 15

c) The difference between the actual rate of return on a risky asset and the actual risk-free rate

Question 16

What is the risk premium?

a) The actual value of the excess return
b) The expected value of the historical return
c) The expected value of the excess return
d) The actual value of historical return

Answer 16

c) The expected value of the excess return

The risk premium is the extra component expected from an investor who takes risk. The degree of risk-aversity from the investor, determines the size of the risk premium.

Question 17

The SD of the excess return is a measure of what?

a) Historical returns
b) Holding period return
c) Risk
d) Expected return

Answer 17

c) Risk

Question 18

There must always be a _________ risk premium on stocks in order to induce risk-averse investors to hold the existing supply of stocks instead of placing all their money in risk-free assets.

a) Negative
b) Positive
c) Neutral
d) It is subordinate

Answer 18

b) Positive

Question 19

What is true about the normal distribution (several answers)?

a) The normal distribution is very easy in use, because you only need 2 parameters: the mean and standard deviation
b) A smaller SD means that possible outcomes cluster more tightly around the mean, while a higher SD implies more diffuse distributions
c) A higher SD means that possible outcomes cluster more tightly around the mean, while a lower SD implies more diffuse distributions
d) The likelihood of realizing any particular outcome when sampling from a normal distribution is fully determined by the number of standard deviations that separate that outcome from the mean
e) The shorter horizon, the closer we get to the normal distribution.
f) The longer horizon, the closer we get to the normal distribution.

Answer 19

distribution (several answers)?

a) The normal distribution is very easy in use, because you only need 2 parameters: the mean and standard deviation
b) A smaller SD means that possible outcomes cluster more tightly around the mean, while a higher SD implies more diffuse distributions
d) The likelihood of realizing any particular outcome when sampling from a normal distribution is fully determined by the number of standard deviations that separate that outcome from the means
f) The longer horizon, the closer we get to the normal distribution.

Question 20

When the distribution is _______ skewed (skewed to the right) the standard deviation _____ risk. Conversely, when the distribution is _____ skewed (skewed to the left), the SD will ______ risk.

a) underestimate
b) positively
c) negatively
d) overestimates

Answer 20

When the distribution is (b) positively skewed (skewed to the right) the standard deviation (d) overestimates risk, because extreme positive surprises (which do not concern investors) nevertheless increase the estimate of volatility. Conversely, when the distribution is (c) negatively skewed (skewed to the left), the SD will (a) underestimate risk.

Question 21

What does kurtosis measure?

a) The maximum loss that is exceeded, over the time horizon, only with the chosen probability
b) The degree of ‘high’ tails
c) The degree of fat tails
d) The ratio of the average cubed deviations from the sample average

Answer 21

c) The degree of fat tails

Question 22

What is the kurtosis for a normal distribution defined as?

a) Kurtosis = 0
b) Kurtosis < 0
c) Kurtosis > 0
d) This cannot be said without knowing the values of mean and SD

Answer 22

a) Kurtosis = 0

Kurtosis above zero is a sight of fatter tails.

Question 23

What does VaR (Value at Risk) measure?

a) The loss that will be exceeded with a specified probability such as 1% or 5%.
b) The expected rate of return conditional on the portfolio falling below a certain value.
c) The ratio of the average cubed deviations from the sample average, called the third moment, to the cubed standard deviation.
d) The expected loss on a short position

Answer 23

a) The loss that will be exceeded with a specified probability such as 1% or 5%.

Question 24

Suppose the real interest rate is 3% per year and the expected inflation rate is 8%. What is the nominal interest rate?

a) 5%
b) 4,85%
c) 11%
d) 11,24%

Answer 24

d) 11,24%

r_nom=(1+r_real)/(1+i)-1=(1+0,03)/(1+0,08)-1=11,24%

Question 25

A bank offers two alternative interest schedules for a savings account of $100.000 locked in for 3 years: (a) a monthly rate of 1%; and (b) an annually, continuously compounded rate, r_cc, of 12%. Which alternative should you choose?

a) EAR_a=(1+r)^12-1=(1+0,01)^12-1=12,68%
b) EAR_b=e^r-1=e^0,12-1=12,75%
c) None of the alternatives are a good investment
d) It is not possible do make an investment decision on the known criteria

Answer 25

b) EAR_b=e^r-1=e^0,12-1=12,75%

You should always choose the alternative with the higher EAR, hence the continuously compounded rate at 12% should be chosen.

Question 26

You are considering two alternative two-year investments: You can invest in a risky asset with a positive risk premium and returns in each of the two years that will be identically distributed and uncorrelated, or you can invest in the risky asset for only one year and then invest the proceeds in a risk-free asset. Which of the following statements about the first investment alternative (compared with the second) are true?

a) Its two-year risk premium is the same as the second alternative.
b) The standard deviation of its two-year return is the same.
c) Its annualized standard deviation is lower.
d) Its Sharpe ratio is higher.
e) It is relatively more attractive to investors who have lower degrees of risk aversion.

Answer 26

c) Its annualized standard deviation is lower

Let σ= the annual SD of the risky investments and σ_1= the standard deviation of the first investment alternative over the two-year period. Then,
σ_1=√2*σ
Therefore, the annualized standard deviation for the first investment alternative is equal to:
σ_1/2=σ/√2

e) It is relatively more attractive to investors who have lower degrees of risk aversion.

The first investment alternative is more attractive to investors with lower degrees of risk aversion. The first alternative (entailing a sequence of two identically distributed and correlated risky investments) is riskier than the second alternative (the risky investment followed by a risk-free investment). Therefore, the first alternative is more attractive to investors with lower degrees of risk aversion.

Question 27

Business become more pessimistic about future demand for their products and decide to reduce their capital spending. This will _______ the equilibrium real rate of interest.
Households are induced to save more because of increased uncertainty about their future Social Security benefits. This will cause the the equilibrium real rate of interest to _______ .
The Federal Reserve Board undertakes open-market purchases of U.S. Treasury securities in order to increase the supply of money. The equilibrium real rate of interest will ______ .

a) Rise, rise, rise
b) Decrease, rise, rise
c) Decrease, Fall, rise
d) Decrease, fall, fall

Answer 27

d) Decrease, fall, fall

If businesses reduce their capital spending, then they are likely to decrease their demand for funds. This will shift the demand curve to the left and reduce the equilibrium real rate of interest.

Increased household saving (increases the supply of funds available for lending) will shift the supply of funds curve to the right and cause real interest rates to fall.

Open market purchases of U.S. Treasury securities by the Federal Reserve Board are equivalent to an increase in the supply of fund and a shift of the supply curve to the right. The equilibrium real rate of interest will decrease.

Question 28

You are considering the choice between investing $50,000 in a conventional 1-year bank CD offering an interest rate of 5% and a 1-year “Inflation-Plus” CD offering 1.5% per year plus the rate of inflation.
Which is the safer investment?

a) Both is equally safe
b) The “Inflation-Plus” CD
c) The conventional 1-year bank CD
d) This cannot be determined

Answer 28

b) The “Inflation-Plus” CD

The ‘inflation-plus’ CD is the safer investment because it guarantees the purchasing power of the investment. Using the approximation that the real rate equals the nominal rate minus the inflation rate, the CD provides a real rate of 1,5% regardless of the inflation rate. The investor will be appropriately compensated for any level of inflation rate to materialize over the next year.

Question 29

You are considering the choice between investing $50,000 in a conventional 1-year bank CD offering an interest rate of 5% and a 1-year “Inflation-Plus” CD offering 1.5% per year plus the rate of inflation. Which offers the higher expected return?

a) Both offers the same return
b) The “Inflation-Plus” CD
c) The conventional 1-year bank CD
d) This cannot be determined

Answer 29

d) This cannot be determined

The expected return depends on the expected rate of inflation over the next year. If the expected rate of inflation is less than 3,5% then the conventional CD offers a higher real return than the Inflation-Plus CD; if the expected rate of inflation is greater than 3,5%, then the opposite is true. In conclusion, the expected return on each investment depends on the expected inflation rate.

Question 30

You are considering the choice between investing $50,000 in a conventional 1-year bank CD offering an interest rate of 5% and a 1-year “Inflation-Plus” CD offering 1.5% per year plus the rate of inflation. If you expect the rate of inflation to be 3% over the next year, which is the better investment?

a) Both offers the same return
b) The “Inflation-Plus” CD
c) The conventional 1-year bank CD
d) This cannot be determined

Answer 30

d) This cannot be determined

If you expect the rate of inflation to be 3% over the next year, then the conventional CD offers you an expected real rate of return of 2%, which is 0,5% higher than the real rate on the inflation-protected CD. But unless you know that inflation will be 3% with certainty, the conventional CD is also riskier. The question of which is the better investment depends on your attitude towards risk vs. return. You might choose to diversify and invest part of your funds in each.

Question 31

You are considering the choice between investing $50,000 in a conventional 1-year bank CD offering an interest rate of 5% and a 1-year “Inflation-Plus” CD offering 1.5% per year plus the rate of inflation. If we observe a risk-free nominal interest rate of 5% per year and a risk-free real rate of 1.5% on inflation-indexed bonds, can we infer that the market’s expected rate of inflation is 3.5% per year?

a) Yes
b) No
c) Sometimes
d) This cannot be determined

Answer 31

b) No

E(r)_CD>E(r)_CD^(Inflation Plus)→2%>1.5%

We cannot assume that the entire difference between the risk-free nominal rate of 5% and the real risk-free rate of 1,5% is the expected rate of inflation. Part of the difference is probably a risk premium associated with the uncertainty surrounding the real rate of return on the conventional CDs. This implies that the expected rate of inflation is less than 3,5% per year.

Question 32

The continuously compounded annual return on a stock is normally distributed with a mean of 20% and standard deviation of 30%. With 95.44% confidence, we should expect its actual return in any particular year to be between which pair of values?

a) −40.0% and 80.0%
b) −30.0% and 80.0%
c) −20.6% and 60.6%
d) −10.4% and 50.4%

Answer 32

a) −40.0% and 80.0%

Upper=20%+(2*30%)= 80%
Lower=20-(2*30%)= - 40%

Explanation of why two standard deviations from the mean: The 68-, 95- and 99,7 – rule. Under this rule, 68% of the data falls within one SD, 95% within 2 SD and 99,7% within three SD from the mean.

Question 33

How is the expected annual HPR (holding period return) calculated?

a) Expected Annual HPR=risk-free rate + average risk premium for a given period
b) Expected Annual HPR=risk-free rate - average risk premium for a given period
c) Expected Annual HPR=Market return + average risk premium for a given period
d) Expected Annual HPR=Market return - average risk premium for a given period

Answer 33

a) Expected Annual HPR=riskfree rate+average risk premium for a given period

Question 34

An economy is making a rapid recovery from steep recession, and businesses foresee a need for large amounts of capital investment. How would this development affect real interest rates?

a) Real interest rates are expected to fall
b) Real interest rates are expected to be held constant
c) This cannot be determined
d) Real interest rates are expected to rise

Answer 34

d) Real interest rates are expected to rise

The investment activity will shift the demand for funds curve to the right. Therefore, the equilibrium real interest rate will increase.

Question 35

What is the daily VaR given the following? (i) Probability of P = 2.5%, (ii) Annual volatility σ=20% and (iii) The value of an investment is equal to €15m

a) 5.880.000
b) 4.935.000
c) 370.400
d) 310.905

Answer 35

c) 370.400

VaR=Initial InvestmentVolatility_HorizonProbability level

Yearly Volatility→Daily Volatility =(0.2)/√250=1.26%

VaR_(P=2.5%)=15.000.0001,26%1,96=370.400

Question 36

A security market line (SML) plots:

a) the returns of one security against the return of another security: a pair of returns
b) the excess return on a security over the risk-free rate as a function of the excess return on the market over the risk-free rate.
c) the expected return of the asset against the systematic risk
d) the excess return on a security against its price

Answer 36

c) the expected return of the asset against the systematic risk

The SML is a graphical representation of the expected return–beta (systematic risk) relationship.

Question 37

An economy is making a rapid recovery from steep recession, and businesses foresee a need for large amounts of capital investment. How would this development affect real interest rates?

a) Rise, due to positive shift in the supply curve
b) Decrease, due to negative shift in the demand curve
c) Rise, due to positive shift in the demand curve
d) Rise, due to negative shift in the supply curve

Answer 37

c) Rise, due to positive shift in the demand curve
Real interest rates are expected to rise. The investment activity will shift the demand for funds curve to the right. Therefore, the equilibrium real interest rate will increase.