Q1. (19 marks)

Consider the following table, which gives a security analyst's expected return on two stocks for two particular market returns:

a. What are the betas of the two stocks? (2 marks)

b. Later when more information about the market comes out, the analyst is almost certain that the market return for the next year will be 10%. Calculate the expected returns for stocks A and B. (4 marks)

c. If both stocks A and B lie on the SML, draw the SML and label the axes and any important points. (3 marks)

d. The standard deviations for Stock A and B are 24% and 15%, and the correlation between the two stocks is 0.2. The optimal risky portfolio using only stocks A and B can be formed by allocating 63% funds in A and 37% in B. Assume the expected market return for the next year will be 10% and the market standard deviation will be 17.1%. Draw the CAL and CML and label the axes and any important points. (6 marks)

e. If you can invest in any risky assets (not limited to stocks A and B) and risk-free assets, how would you construct your portfolio to achieve an expected return of 12%? Assume the expected market return will be 10% next year. (4 marks)

Answer:

a.  Beta_A = (18.4-8.8)/(16-8)=1.2

Beta_B = (8.8-5.6)/(16-8)=0.4

b. 8.8%=Rf+1.2*(8%-Rf)

Rf=4%

E(rA) = 4% + 1.2 (10%-4%) = 11.2%

E(rB) = 4% + 0.4 (10%-4%) = 6.4%

.

11.2% 10% 6.4%

rf=4%

β

0.4                 1              1.2

d. E(rp) = 63%*11.2% + 37%*6.4% =9.42%

  = 0.632  ∗ 0.242  + 0.372  ∗ 0. 152  + 2 ∗ 0.63 ∗ 0.37 ∗ 0.2 ∗ 0.24 ∗ 0. 15 = 17. 1%

17.1%

.

w1*rf + (1-w1)*rm = 12%

w1*4% + (1-w1)*10%=12%

w1 =-33.33%

Borrow 33.33% at risk-free rate and invest the full amount (the investor’s own fund and the borrowing) in market portfolio.

Q2. (19 marks)

Answer the following questions:

i. Compare and contrast the geometric average return and the arithmetic average return. Discuss the advantages and disadvantages of each. (6 marks)

ii. XYZ's stock price and dividend history are as follows:

Year       Beginning-of-Year Price Dividend Paid at Year-End

2018

2019

2020

2021

122

146

110

122

4

4

4

4 

An investor buys three shares of XYZ at the beginning of 2018, buys another two shares at the beginning of 2019, sells one share at the beginning of 2020, and sells all four remaining shares at the beginning of 2021. What are the arithmetic and geometric average time-weighted rates of return for the investor? (7 marks)

iii. What are some of the potential reasons of an upward sloping yield curve? What are some of the potential reasons of a downward sloping yield curve? (6 marks)

Answer:

i. Arithmetic average return is a simple interest rate of return. It is calculated by diving the sum of HPR for each period over the investment horizon by the number of periods.

The geometric average return formula is a way to calculate the average rate of return on an investment that is compounded over multiple periods. It is also understood as IRR. Arithmetic average:

•   Easy to calculate and understand

•    Bias return upwards

Geometric average:

•   Tells you the compound rate of return you will get over the investment horizon, which is what the investors are interested to know

•   Hard to calculate and understand

•   Assumes a reinvestment rate same as the IRR, which is less realistic

ii.  Time-weighted  average  returns  are  based  on  year-by-year  rates  of  return:

Year   Return = (Capital gains + Dividend)/Price

2018 – 2019

2019 – 2020

2020 – 2021

[($146 − $122) + $4]/$122 = 22.95%

[($110 − $146) + $4]/$146 = −21.92%

[($122 − $110) + $4]/$110 = 14.55%

Arithmetic mean: (22.95% − 21.92% + 14.55%)/3 = 5. 19%

Geometric mean:  (1.2295 × 0.7808 × 1.1455)1/3 − 1 = 0.0322 = 3.22% iii.

Upward sloping:

•   Risk and uncertainty about the future (long-term investment)

•   Expectation on a rising interest rate in the future

•   Inflation

•   Liquidity premium

•   Possible segmentation: more supply in the long-term market

•   …

Downward sloping:

•   expectation on a lower interest rate in the future

•   Deflation

•   Possible segmentation: more supply in the short-term market

•   …

Q3.  (10 marks)

A pension fund has a perpetual obligation of $1.4 million per year to its recipients. The yield to maturity on all bonds is 13%.

a. If the duration of 5-year maturity bonds with coupon rates of 9% (paid annually) is four years and the duration of 20-year maturity bonds with coupon rates of 6% (paid annually) is 11 years, how much of each of these coupon bonds (in market value) will you want to hold to both fully fund and immunize your obligation? (5 marks)

b. What will be the par value of your holdings in the 20-year coupon bond? (5 marks)

Answer:

a.

PV of obligation = $1.4 million/0.130 = $10.77 million

Duration of obligation = 1.130/0.130 = 8.69 years

Call w the weight on the five-year maturity bond (which has duration of four years).

Then:

(w × 4) + [(1 − w) × 11] = 8.69 ⇒⇒ w = 0.3297

Therefore: 0.3297 × $10.77 = $3.55 million in the 5-year bond and

0.6703 × $10.77 = $7.22 million in the 20-year bond.

.

The price of the 20-year bond is:

[$60 × Annuity factor (13.0%, 20)] + [$1,000 × PV factor (13.0%, 20)] = $508.27 Therefore, the bond sells for 0.508 times its par value, and:

Market value = Par value × 0.508

$7.22 million = Par value × 0.508 ⇒⇒ Par value = $14.20 million

Another way to see this is to note that each bond with par value $1,000 sells for

$508.267. If total market value is $7.22 million, then you need to buy approximately 14,200 bonds, resulting in total par value of $14.20 million.

Q4. (11 marks)

A money manager’s performance in a recent month is presented in the table below.

a. What was the manager’s return in the month? What was her overperformance or underperformance? (3 marks)

b. What was the contribution of security selection to relative performance? (4 marks)

c. What was the contribution of asset allocation to relative performance? (4 marks)

Answer:

a.

Bogey: (0.6 × 2.6%) + (0.3 × 2.3%) + (0. 1 × 0 .7%) =2.32%

Actual: (0.5 × 2. 1%) + (0. 1 × 1.9%) + (0.4 × 0 .6%) =1.48   

Underperformance:        0.84%

.

Security Selection:

0.5

0.1

0.4

Contribution of security selection:          -0.33%

.

Asset Allocation:

Equity

Bonds

Cash

-0.1%

-0.2

0.3

2.6%

2.3

0.7

-0.26%

-0.46

0.21

Contribution of asset allocation:         -0.51% 

Summary: (this step is not necessary)

Security selection

Asset allocation

Q5. (8 marks)

Consider the following data for a one-factor economy. All portfolios are well diversified.

Would an arbitrage opportunity exist? If so, what would be the arbitrage strategy?

Answer:

The expected return for portfolio B equals the risk-free rate since its beta equals 0. For portfolio A, the ratio of risk premium to beta is (14 − 4)/1.2 = 8.33                   For portfolio C, the ratio is lower at (8 – 4)/0.8 = 5

This implies that an arbitrage opportunity exists. For instance, you can create a portfolio D with beta equal to 0.8 (the same as C’s) by combining portfolio A and portfolio B

Beta_c/Beta_a=0.8/1.2=66.67%

Therefore, invest 66.67% in A and 33.33% in C

The expected return and beta for portfolio D are then:

E(rG ) = (0.6667 × 14%) + (0.3333 × 8%) = 9.33%

βD = (0.6667 × 1.2) + (0.3333 × 0) = 0.8

Comparing portfolio D to portfolio B, D has the same beta and higher return. Therefore, an arbitrage opportunity exists by buying portfolio D through buying 66.67% A and 33.33% C and selling an equal amount of portfolio B. The profit for this arbitrage will be

rD – rB =9.33% - 8% = 1.33%

Q6. What are the assumptions for CAPM? Is CAPM still a reliable and accurate model if some of the assumptions are violated? (11 marks)

Assumptions:

•   There is no tax or transaction cost

•   Investors are price-takers with wealth that is small relative to total wealth in the market: this suggests that investments made individual investors are small enough and so would not affect the market.

•   Focus on a single-period investment horizon: the standard CAPM applies to single-period investment only. With multiple-period investment, there will be a lot of other issues to consider and therefore would complicate the model significantly.

•   Can  only purchase publicly traded  assets: No private  assets  are  considered under the CAPM

•   Can borrow and lend at the risk-free rate: Only one rate is used for all lending and borrowing activities for all individuals and firms, disregard their credit worthiness.

•   Investors  are rational  mean-variance optimisers,  so will use the Markowitz portfolio selection model: this assumption is here to ensure that all investors are rational investors who will make investments in the same direction.

•   Have  homogenous  expectations:  Homogeneous  expectations  are  consistent with the assumption that all relevant information is publicly available.

Violations:

Apparently, most of the assumptions under CAPM would not hold in practice. For example:

•   The assumption of homogenous expectation appears ominously restrictive, but it actually is not all that problematic. When most information is public, it would not be uncommon for investors to be close to agreement on firms’ prospects. Moreover, trades of investors who derive different input lists will offset and prices will reflect consensus expectations.

•   Assumption of no tax:

Two investors can realize different after-tax returns from the same stock. Such distortions to the  “input list”  could, in principle, lead to  different  after-tax optimal risky portfolios; hence, the CAPM required the assumption ofno taxes. Nevertheless, despite  an extension to the CAPM that incorporates personal taxes on dividends and capital gains, there is no decisive evidence that taxes are a major factor in stock returns.

Empirical tests of the CAPM yielded the following results:

Early  evidence  suggested  that  non-systematic  risk  was  significant  in  explaining security returns, a finding inconsistent with the CAPM;

More  recent  evidence,  which  controlled  for  error  in  the  measurement  of  beta, contradicted earlier tests, finding that non-systematic risk did not explain security returns. However, the SML estimated in providing this evidence was too flat relative to that predicted by the CAPM; and,

The market index outperforms the majority of professionally managed portfolios, consistent with the efficiency of the former as well as with the CAPM.

Q7. (10 marks)

Answer the following questions:

i. Do we expect to observe the strong form of efficient market in practice? Explain. (5 marks)

ii. Post earnings announcement drift is an anomaly where stock prices continue to move in the same direction of the earnings surprise for several months following an earnings  announcement.  Which  form  of efficient  market  does  the  post  earnings announcement drift violate? Explain. (5marks)

Answer:

i. The strong form of efficient market states that any private information should be incorporated into security prices in an instantaneous and unbiased manner.

It would not be surprising if insiders were able to make superior profits trading in their firm’s stock. In other words, we do not expect markets to be strong-form efficient; we regulate and limit trades based on inside information.

ii. PEAD violates the semi-strong form of efficient market. The semi-strong form of efficient  market  states  that  any  public  information  should  be  incorporated  into security prices in an instantaneous and unbiased manner. PEAD is a delayed investors’

reaction to earnings announcement, which is public firm information. Q 8. (12 marks)

Read the article titled ‘Black Rock’s secret hedge fund star gets paid more than its CEO’ published  on  29  Oct,  2021 in  Financial  Review below,  and  answer the following questions.

“Alister Hibbert is one of Black Rock’s best kept secrets. He’s the money manager whose hedge fund has enriched the firm, its clients and himself with a near 370 per cent gain over the past decade.

Hibbert, 51, has often been the firm’s highest paid employee globally. Last year alone, he earned a nine-figure sum more than triple the size of CEOLarry Fink’s $US30 million ($39.8 million) payout …”

a)  What  is  the  implication  of  Hibbert’s  performance  under  the  efficient  market hypothesis? (4 marks)

b) When measuring a manager’s investment performance, we should measure it over an entire market cycle. Do you agree with this statement? Explain. (4 marks)

c) Discuss the fee structure in hedge funds. What is the issue with the fee structure and what is the possible solution to it? (Note: this is a general question, not specifically related to the article.) (4 marks)