FIN2004 Tutorial 3Jiten Khemlani / Victoria Iskak/

Jomel Ho / Guo Si

RWJ Chap 12 Qn 9a

9. You've observed the following returns on Crash-n-Burn Computer's stock over the past five years: 7 percent, –12 percent, 11 percent, 38 percent, and 14 percent.

a. What was the arithmetic average return on Crash-n-Burn’s stock over this five-year period?

To find the average return, we sum all the returns and divide by the number of returns, so:Average return = (.07 –.12 +.11 +.38 +.14)/5 = .1160 or 11.60%

RWJ Chap 12 Qn 9b

9. b. What was the variance of Crash-n-Burn’s return over his period? The standard deviation?

(1) Actual Return

(2) Average Return

(3) Deviation (1) – (2)

(4) Squared Deviation

0.07 0.116 -0.046 0.002116

-0.12 0.116 -0.236 0.055696

0.11 0.116 -0.006 3.6 x

0.38 0.116 0.264 0.069696

0.14 0.116 0.024 0.000576

Totals 0.58 0.000 0.12812

RWJ Chap 12 Qn 9b

Using the equation to find Variance,

Variance = 1/4[(.07 – .116)^2 + (–.12 – .116)^2 + (.11 – .116)^2 + (.38 – .116)^2 +(.14 – .116)^2]

Variance = 0.032030

So, the standard deviation is:Standard deviation = (0.03230)^(1/2) = 0.1790 or 17.90%

RWJ Chap 12 Qn 10a

10. For the problem above, suppose the average inflation rate over this period was 3.5 percent and the average rate T-bill rate over the period was 4.2 percent.

a. What was the average real return on Crash-n-Burn’s stock?

To calculate the average real return, we can use the average return of the asset, and the average inflation in the Fisher equation. Doing so, we find:

(1 + R) = (1 + r)(1 + h)r = (1.160/1.035) – 1 = .0783 or 7.83%

RWJ Chap 12 Qn 10b

b. What was the average nominal risk premium on Crash-n-Burn’s stock?

• The average risk premium is simply the average return of the asset, minus the average risk-free rate, so, the average risk premium for this asset would be:

RP = R – Rf = .1160 – .042 = .0740 or 7.40%

RWJ Chap 12 Qn 11

11. Given the information in the problem just above, what was the average real risk-free rate over this time period? What was the average real risk premium?

We can find the average real risk-free rate using the Fisher equation. The average real risk-free rate was:(1 + R) = (1 + r)(1 + h)rf = (1.042/1.035) – 1 = .0068 or 0.68%

Average real risk premium can be found by subtracting the average risk-free rate from the average real return. rp = r – rf = 7.83% – 0.68% = 7.15%

RWJ Chap 12 Qn 16

16.

Year Price Dividend Dollar Return

% Return 1 + r

1 $60.18 - - - 1

2 73.66 $0.60 $14.08 0.23396 1.23396

3 94.18 0.64 21.16 0.28726 1.28726

4 89.35 0.72 -4.11 -0.0436 0.9564

5 78.49 0.80 -10.06 -0.11259 0.88874

6 95.05 1.20 17.76 0.22627 1.22627

RWJ Chap 12 Qn 16

16. Arithmetic average return :RA = (0.2340 + 0.2873 – 0.0436 – 0.1126 + 0.2263)/5 = 0.1183 or 11.83%

Geometric average return:RG = [(1 + .2340)(1 + .2873)(1 – .0436)(1 –.1126)(1 + .2263)]^(1/5) – 1 = 0.1058 or 10.58%

RWJ Chap 13 Qn 23

23. Consider the following information on three stocks:

a. If your portfolio is invested 40 percent each in A and B and 20 percent in C, what is the portfolio expected return? The variance? The standard deviation?

b. If the expected T-bill rate is 3.80 percent, what is the expected risk premium on the portfolio?

c. If the expected inflation rate is 3.50 percent, what are the approximate and exact expected real returns on the portfolio? What are the approximate and exact expected real risk premiums on the portfolio?

RWJ Chap 13 Qn 23a

• Boom: E(Rp) = .4(.24) + .4(.36) + .2(.55) = .3500 or 35.00%

• Normal: E(Rp) = .4(.17) + .4(.13) + .2(.09) = .1380 or 13.80%

• Bust: E(Rp) = .4(.00) + .4(–.28) + .2(–.45) = –.2020 or –20.20%

Expected return of porfolio:• E(Rp) = .35(.35) + .50(.138) + .15(–.202) = .1612 or

16.12%

RWJ Chap 13 Qn 23a, b

• Variance = .35(.35 – .1612)^2 + .50(.138 – .1612)^2 + .15(–.202 – .1612)^2= .03253

• Therefore, St Dev = (.03253)^(1/2) = .1804 or 18.04%

b) The risk premium is the return of a risky asset, minus the risk-free rate. T-bills are often used as the risk-free rate, so:RPi = E(Rp) – Rf = .1612 – .0380 = .1232 or 12.32%

RWJ Chap 13 Qn 23 c

• The approximate expected real return is the expected nominal return minus the inflation rate, so:

Approximate expected real return = .1612 – .035 = .1262 or 12.62%

• To find the exact real return, we will use the Fisher equation. Doing so, we get:

1 + E(Ri) = (1 + h)[1 + e(ri)]1.1612 = (1.0350)[1 + e(ri)]e(ri) = (1.1612/1.035) – 1 = .1219 or 12.19%

• Approximate real risk premium= expected return - risk-free rate, so:

Approximate expected real risk premium = .1612 – .038 = .1232 or 12.32%

Exact expected real risk premium = Approximate expected real risk premium / (1+ inflation rate), so:

Exact expected real risk premium = .1168/1.035 = .1190 or 11.90%

RWJ Chap 13 Qn 23 c

THANK YOU