What is the appropriate measure of risk for a portfolio of assets with normally distributed returns?

What is the appropriate measure of risk for a portfolio of assets with normally distributed returns?

HOLDING PERIOD RETURN:

1. You purchased 1492.50 shares of Gimwraxx stock for $104.44. You sold the stock 316.5 days later for $120.99. During that holding period, a dividend of $3.25 was paid. What is your holding period return (HPR)?
2. Would your holding period return go up or down if Gimwraxx paid an additional dividend after the holding period?
3. Your holding period return was 15.50% for your latest investment in Gimwraxx stock. You purchased the stock at $120 and received a $5 dividend during your holding period. What price did you sell the stock for?
4. What is the difference between the Total Return formulas & the Holding Period Return formulas?

ARITHMETIC AVERAGE & GEOMETRIC AVERAGE

Arithmetic average = (R1 + R2 + … + Rn) / n

Geometric Average Return = ((1 + R1) × (1 + R2) × … × (1 +Rn))(1/n) – 1

1. I earned 2%, 13%, 2%, and 13% in quarters 1, 2, 3, and 4 respectively on my Gimwraxx stock. What is my rate of return for the year if I use the arithmetic average method? If I use the geometric average method?
2. I earned 2%, -13%, -2%, and 13% in quarters 1, 2, 3, and 4 respectively on my Gimwraxx stock. What is my rate of return for the year if I use the arithmetic average method? If I use the geometric average method?
3. Why is the arithmetic average return different from the geometric average return? Which one is higher?
4. What is the difference between time-weighted average return and geometric average return?
5. Given the following chart, what is the dollar-weighted return for the year? (Challenge Question – use CF button on calculator)

1st Quarter

2nd Quarter

3rd Quarter

4th Quarter

Assets under management at start of quarter

10

12.3

14.215

9.4828

Holding-period return (%)

8

5

−15

9

Total assets before net inflows

10.8

12.915

12.083

10.336

Net inflow ($ million)

1.5

1.3

−2.6

0.4

Assets under management at end of quarter

12.3

14.215

9.4828

10.736

1. How does the internal rate of return (IRR) compare with the dollar-weighted return?

ANNUALIZING RATES OF RETURN

Annual percentage rate = APR = Per-period rate × Periods per year

Effective annual rate = EAR =

1. My quarterly (per-period) rate is 1.22%. What is my APR? EAR?
2. My monthly (per-period) rate is 0.2315% What is my APR? EAR?
3. My semi-annual (per-period) rate is 2.5% What is my APR? EAR?
4. I have an investment that has an APR of 5.65% and is continuously compounded. What is my EAR?
5. I have an investment that is continuously compounded with an EAR of 4.96%. What is my APR?

INFLATION AND THE REAL RATE OF INTEREST

r approximately equals R – i

Nominal Interest and Real Interest formula:

(Alternative formula: 1+R = (1 + r)(1 + i))

1. Nominal rate is 7%, inflation rate is 1.5%. What is the real rate using the approximate method? Using the formula?
2. Nominal rate is 3.0%, inflation rate is 3.5%. What is the real rate using the approximate method? Using the formula?
3. Real rate is 4.2%, inflation rate is 1.9%. What is the nominal rate using the approximate method? Using the formula?
4. Real rate is 5.9%, inflation rate is 12.3%. What is the nominal rate using the approximate method? Using the formula?
5. Challenge question: Real rate is 4.4%, nominal rate is 6.9%. What is the inflation rate using the approximate method? Using the formula?
6. What is the appropriate measure of risk for a portfolio of assets with normally distributed returns?

a. Expected return

b. Real rate of return

c. Standard deviation

d. VaR

1. What two statistics completely describe the normal distribution?

a. Mean and variance.

b. Mean and standard deviation.

c. Median and mode

d. Leptokurtosis and Platykurtosis

1. Value at risk (VaR) is a measure of what?

a. Excess risk beyond expected return

d. Upside risk

c. Amount of return per unit of risk

d. Downside risk at a selected probability

1. Risk premium =

a. E(rp) – rf

b. Expected return on the portfolio

c. Risk-free rate of return

d. Expected return of the market

1. Expected return is 5.26%; risk-free rate is 1.1%, standard deviation of portfolio is 8.95% What is the Sharpe Ratio of the portfolio?
2. Expected return is 12.33%; risk-free rate is 5.52%, standard deviation of portfolio is 26.5% What is the Sharpe Ratio of the portfolio?
3. Portfolio risk premium is 8.5%; risk-free rate is 1.5%, standard deviation of portfolio is 12.1% What is the Sharpe Ratio of the portfolio?
4. Portfolio risk premium is 4.23%; risk-free rate is 0.52%, standard deviation of portfolio is 42.1% What is the Sharpe Ratio of the portfolio?
5. Which portfolio of the four above in questions 25-29 is the best investment (think Sharpe about this one…)?
6. The following can be considered as risk-free assets:

a. T-bill only

b. T-bills, T-bonds, money market funds

c. Money market funds only

d. S&P 500 stock index fund

1. Risk averse investors would have a (higher/lower) percentage of risk free assets compared to risky assets than a risk neutral investor?
2. Risk seeking investors would have a (higher/lower) percentage of risk free assets compared to risky assets than a risk neutral investor?
3. The trade-off line between risky and risk-free assets is called:

a. The Capital Market Line

b. The Capital Allocation Line

c. The efficient frontier

d. The normal distribution

1. Given an expected return of the risky asset portion of your portfolio of 7.6%, and the expected return of the risk-free asset of 1.5%, what is the expected return of the complete portfolio if you have 35% of your assets in the risky portfolio? What is the standard deviation of the complete portfolio?
2. Given an expected return of the risky asset portion of your portfolio of 10.2%, and the expected return of the risk-free asset of 0.5%, what is the expected return of the complete portfolio if you have 75% of your assets in the risky portfolio? What is the standard deviation of the complete portfolio?
3. If you increased the percentage of risky assets in your portfolio would you expect your return to go up or down? Would your risk go up or down?
4. If you wanted to maximize your return, what percentage would you put into the risky asset? What would that do to your risk?
5. The following are advantages of a passive investment strategy

a. Passive investing is simple and inexpensive

b. Misses out on higher returns gained by an active strategy

c. Requires multiple funds and complex portfolio strategies

d. Ideal for risk-seeking investors

1. The Capital Market Line (CML) is:

a. The capital allocation line using a mix of stock and bond funds without risk-free assets

b. The capital allocation line using a market-index portfolio as the risky asset

c. The capital allocation line using only the risk-free asset

d. The capital allocation line using historical bond fund returns only to calculate the line

1. The answer to question #23 is always:

a. A

b. D

c. B

d. C

1For n periods of compounding:(1)1[(1)1]compounding per periodnnAPREARnAPREARnwheren

For Continuous Compounding:

1

ln(1)

APR

EARe

APREAR

=-

=+

1

1

1

Real Interest Rate

Nominal Interest Rate

Inflation Rate

R

r

i

where

r

R

i

+

+=

+

=

=

=

()

Portfolio Risk Premium

Standard Deviation of Excess Returns

()Expected Return of the portfolio

Risk Free rate of return

Standard Deviation of portfolio excess r