SMM510 Portfolio Management

Division of Marks: All questions carry equal marks

Instructions to students: Answer THREE questions out of five

This paper contains FIVE questions and comprises EIGHT pages including the title page

Whether or not there are any other additional materials: None

Your work should be in your own words, it should NOT contain material copied straight from lecture notes, textbooks, or other resources. If you do rely on external sources within your answer, these should be properly referenced/cited.

Students are expected to show all necessary workings to obtain their final solution. If this is not done, then marks will be deducted even when the correct numerical solution is obtained.

Internal Examiner: Dr Natasha Todorovic External Examiner: Professor Sunil Poshakwale

Question 1

You are presented with two US long-only equity funds that benchmark against S&P 500 Index. Their performance characteristics are as follows:

Portfolio Characteristics	Fund 1	Fund 2
Carhart Alpha monthly (p‐values in	0.005	‐0.01
parentheses)	(0.03)	(0.11)
Jensen’s Alpha monthly (p‐values in	0.02	‐0.003
parentheses)	(0.001)	(0.56)
Angelidis et al. (2012) benchmark‐	0.001	‐0.005
adjusted alpha monthly (p‐values in parentheses)	(0.15)	(0.03)
Treynor and Mazuy market‐timing	0.034	‐0.001
coefficient (p‐values in parentheses)	(0.09)	(0.022)

Interpret the Carhart alpha and the Jensen’s alpha for each portfolio and explain the differences between the Carhart (1997) and Jensen (1968) model.

(30 marks)

Interpret the values of the Angelidis et al. (2013) benchmark-adjusted alpha (AGT alpha) for each fund and explain the benefits of this method for performance evaluation. Why has the AGT alpha decreased compared to the Carhart alpha for both funds?

(20 marks)

Explain the reason one shouldn’t use Jensen’s alpha for measuring a market timers’ performance. Which of the two funds has the better market timing ability? Your answer should include the explanation of the Treynor and Mazuy (1966) measure.

(30 marks)

You are given the following information on two long-only UK equity portfolios and their benchmark index:

Portfolio Characteristics	Portfolio A	Portfolio B	FTSE All Share Index
Average excess return (over risk‐free rate) p.a.	‐1%	‐1%	0.2%
Standard deviation p.a.	10%	17%	20%
Skewness	‐1.27	‐0.5	0.01
Kurtosis	5.1	6.7	2.99

Rank Portfolios A and B according to their Sharpe ratio and comment on your ranking. Would you recommend the better ranked portfolio to a client? Explain your answer.

(20 marks)

Question 2

ABC Plc is an established UK company with operations throughout UK and Europe. Assume that it is operating in the growing industry and the booming economy. Its employees are covered by defined benefit pension plan which is currently underfunded (with £9bn assets and £10bn liabilities). The asset classes to be included in this pension fund are bonds, equities and commodities. The average age of ABC’s employees is 41 years.

Suggest what you believe would be the appropriate strategic asset allocation for this fund, using asset classes given in the question and the information provided about the fund. Split any given asset class into relevant sub-classes if you believe it is appropriate. Your suggested allocation should address any liquidity and underfunding issues.

(30 marks)

Would you benchmark the performance of the portfolio you have suggested in a) against its peers (similar pension funds)? Explain.

(10 marks)

Suggest one asset class that you would add to your portfolio in a) and provide a rationale for its inclusion.

(10 marks)

Last year, the asset allocation and returns in this pension fund and the benchmark were as follows:

Asset Class	Benchmark Weight	Return in benchmark (%)	Active Weight	Active Return (%)
Equity	0.50	5.00	0.65	9.00
Bond	0.40	1.50	0.20	1.70
Commodities	0.10	3.20	0.15	3.84

Calculate the total value added of this portfolio and decompose it into security selection, asset allocation and the interaction effect. Define each of the effects.

(30 marks)

If the standard deviation of equity is 12%, of bonds 5% and of commodity 8%, what would be the appropriate risk-parity weights for these three asset classes? Explain.

(20 marks)

Question 3

The following information is given on the ABC index-tracking fund, which is replicating the Market’s Large Cap Index:

ABC uses stratified sampling replication.
The standard deviation of the ABC portfolio is 4% per month and the R-squared of the regression of ABC’s monthly returns on Market’s Large Cap Index monthly returns is 0.989.

Given this information, answer the following questions:

Compare two commonly used methods for the computation of tracking error. What is the tracking error for the ABC index fund, based on the residual risk approach?

(20 marks)

Would you expect the tracking error from a) to be lower than if the ABC fund followed a full replication approach?

(10 marks)

If portfolio ABC was constructed to replicate the Market’s Small Cap Index, would you expect its tracking error to be lower than the one computed in a)?

(10 marks)

Compare stratified sampling and optimisation approaches to indexation.

(30 marks)

The fund manager of ABC index fund would like to enhance the fund’s returns. Why would he want to do that? Suggest how this could be done through i) stock lending

ii) synthetic indexation and iii) the core satellite approach to index tracking. How much of outperformance is he likely to get from the suggested methods?

(30 marks)

Question 4

How is ‘growth at a reasonable price’ (GARP) approach to investing different from pure growth investing? Explain, using an example of your choice.

(20 marks)

The size (SMB) coefficient from the Fama-French (1993) model is positive (value is 0.02) but insignificant, while the style (HML) coefficient is positive (value is 0.25) and statistically significant at 1% level for portfolio XYZ. What does that tell you about the size and style of portfolio XYZ? Explain.

(15 marks)

If the portfolio from b) is a UK portfolio, which index would you use to benchmark its performance?

(10 marks)

Explain the pros and cons of a style rotation strategy, emphasising the issues related to forecasting variables and models used to predict style performance.

(30 marks)

You are a portfolio manager employing a small-large style rotation strategy. You are facing the following scenario:

‐ The GDP is forecasted to decline for the second consecutive quarter.

‐ The risk premium on small cap stocks is higher than in the previous quarter.

‐ The default premium on corporate bonds is increasing.

Would you buy small or large stocks? Explain your answer and outline why the style rotation strategy often results in sector rotation.

(25 marks)

Question 5

The following four bonds are available to you:

Bond	A	B	C	D
Price	99	100	102	105
Coupon	2.5%	4%	6.5%	7%
Modified Duration	0.9 years	4.6 years	4.5 years	9.9 years
Dollar Duration	0.89	4.6	4.59	10.39
Maturity	1.1years	5.4 years	5.1 years	14.5 years
Price Value of a Basis Point	0.0089	0.046	0.0459	0.1039

The yield curve is upward sloping. Short-term interest rates are expected to decrease while the long-term rates are expected to increase. You are allowed to short-sell. Which bond trading strategy would you apply to best exploit the shift in the yield curve described in this scenario? Illustrate how you would apply that strategy using what you believe are two most suitable bonds from the table above if you had £2 M to invest. Explain your rationale and workings.

(25 marks)

Use any three bonds from the table suitable for the construction of 50/50 duration butterfly trade. Construct this butterfly trade for a $1M par value of the bond you decide to sell and explain the rationale and assumptions used in this type of butterfly trade.

(25 marks)

Interpret the beta coefficient of 0.78 in a regression-based butterfly trade and explain why it is needed. Construct such a butterfly trade for the same bonds you have used in b).

(25 marks)

If the long-term bond in a butterfly trade is replaced with another, longer term bond, how would that affect substitutability in the butterfly trade strategy?