FIN354 Specimen Exam Paper Solution PDF

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FINFINSpecimen Examination PaperImpact Investing and Green Finance Time allowed: 2 hours SolutionsFINYou must answer ALL questions. (Total 100 marks)Question 1H 3 Capital is a long-only investment fund with an AUM of $500m. Its current portfolio is expected to yield an 8% return with a standard devi...

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FIN354 Specimen Examination Paper

Impact Investing and Green Finance ___________________________________________________________________________________

Time allowed: 2.5 hours ___________________________________________________________________________________

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FIN354 Copyright © 2021 Singapore University of Social Sciences

Page 1 of 7 Specimen Examination Paper

You must answer ALL questions. (Total 100 marks) Question 1 H3 Capital is a long-only investment fund with an AUM of $500m. Its current portfolio is expected to yield an 8% return with a standard deviation of 4%. The fund is considering changing its portfolio composition to be composed of two asset classes and has generated the following capital market expectations for each asset class: State of Economy

Probability

Boom Normal Recession

0.1 0.6 0.3

Returns Asset Class Asset Class A B 20% 12% 12% 8% -8% 4%

The chief investment officer of H3 Capital proposes a new portfolio that invests $200m in Asset Class A and the rest of the investable funds in Asset Class B. Assess the risk-return tradeoff of the proposed portfolio using the Sharpe ratio and, hence, recommend whether H3 Capital should make that change. The risk-free rate is 2.5%. (23 marks) Marking Guide: Suggested answer for Question 1: Invested dollars in new portfolio of Asset Class B = 500 – 200 = $300m New portfolio weight on Asset Class A = 200/500 = 40% New portfolio weight on Asset Class B = 300/500 = 60% New portfolio return in the event of a boom = 0.4(20%) + 0.6(12%) = 15.2% New portfolio return in the event of a normal economy = 0.4(12%) + 0.6(8%) = 9.6% New portfolio return in the event of a recession = 0.4(–8%) + 0.6(4%) = –0.8% New portfolio expected return = 0.1(15.2%) + 0.6(9.6%) + 0.3(–0.8%) = 7.04% New portfolio variance = 0.1(0.152 – 0.0704)2 + 0.6(0.096 – 0.0704)2 + 0.3(–0.008 – 0.0704)2 = 0.0029 New portfolio standard deviation = 0.00290.5 = 5.39% New portfolio Sharpe ratio = (7.04 – 2.5)/5.39 = 0.84 Existing portfolio Sharpe ratio = (8 – 2.5)/4 = 1.38 The new portfolio is expected to yield a lower risk premium per unit of total risk compared to the existing portfolio and so the change is not recommended. [23 marks]

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Page 2 of 7 Specimen Examination Paper

Question 2 You are the portfolio manager of a boutique equity fund with $15 million to invest. The risk-free rate is 5% and your fund can borrow and lend at the risk-free rate. Your research analyst finds that the investable equity market index against which your fund is benchmarked has an expected return of 10% and standard deviation of 18%. He suggests that you invest 100% of the funds in the equity of JMP Ltd, which claims to be “a technology company that just happens to do banking” with an expected return of 12% and standard deviation of 40%. (a)

If feasible, construct an efficient portfolio that has the same expected return as JMP Ltd. How many dollars should be invested in each asset to construct such a portfolio? (7 marks)

(b)

What is the standard deviation of the portfolio constructed in part (a)? (3 marks)

(c)

If feasible, construct an efficient portfolio that has the same standard deviation as JMP Ltd. How many dollars should be invested in each asset to construct such a portfolio? (7 marks)

(d)

What is the expected return of the portfolio constructed in part (c)? (3 marks)

(e)

Based on your findings from the earlier parts, would you recommend investing 100% of the funds in JMP Ltd? Explain your recommendation. (3 marks)

Marking Guide: Suggested answer for Question 2: (a)

Let x and 1 – x be the weights on the investable market portfolio and the risk-free asset, respectively. Since the portfolio expected return is a weighted-average of the constituent asset returns, 12% = x(10%) + (1 – x)(5%) x = 1.4 1 – x = –0.4 To construct such a portfolio, one would borrow 0.4(15m) = $6m at the risk-free rate and invest 15m + 6m = $21m in the equity index portfolio. [7 marks]

(b)

Given that one of the assets of a two-asset portfolio is risk-free, Variance of portfolio = (1.4)2(0.18)2 Standard deviation of portfolio = 1.4(0.18) = 25.2% [3 marks]

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Page 3 of 7 Specimen Examination Paper

(c)

Let y and 1 – y be the weights on the investable market portfolio and the risk-free asset, respectively. Given that one of the assets of the two-asset portfolio is riskfree, (0.4)2 = y2(0.18)2 y = 2.22 1 – y = –1.22 To construct such a portfolio, one would borrow 1.22(15m) = $18.33m at the riskfree rate and invest 15m + 18.33m = $33.33m in the equity index portfolio. [7 marks]

(d)

Expected return of portfolio = 2.22(10%) – 1.22(5%) = 16.11% [3 marks]

(e)

No, the efficient portfolio in part (a) has the same expected return as JMP Ltd but a lower standard deviation (25.2% vs 40%), while the efficient portfolio in part (c) has the same standard deviation as JMP Ltd but a higher expected return (16.11% vs 12%). [3 marks]

Use the following information for Questions 3 through 5: Sarah is a junior investment adviser of H3 Capital and recently met with a high net worth client, Joe, to prepare an investment policy statement. At the meeting, Joe does not reveal any quantifiable return and risk objectives and Sarah was only able to cobble together the following notes in order to draft a client profile: “Joe Schmoe is a 40-year-old property agent living in the United States, with investable assets of USD20 million. Of this amount, Joe needs about $2 million three months from now in order to make a housing downpayment. He is not a big spender but hopes to fund at least part of his annual expenses, which are highly predictable, from his investment portfolio for the next twenty years. He is concerned, however, about the general increase in the prices of goods and services over time. Furthermore, Joe would like a portfolio that can be liquidated quickly and at fair value. He strongly supports American businesses and would like his investments to primarily contribute to the overall growth of the US economy.” Based on the client profile, Sarah proposes six potential investment portfolios for Joe:

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Page 4 of 7 Specimen Examination Paper

Question 3 Discuss how Joe’s circumstances will affect his allocation to each asset class (low, medium, or high) and, hence, recommend a portfolio that is most suitable for him. No calculations are required. (24 marks) Marking Guide: Suggested answer for Question 3: •

Cash and equivalents: This requires at least a 10% allocation for the impending housing downpayment.

•

US equities: A high allocation because of Joe’s fairly young age and his concern about inflation protection.

•

International equities and bonds: A low allocation because of Joe’s preferences for funding US businesses.

•

US bonds: A low allocation to bonds compared to equities because of his young age, concern about inflation protection, and low recurring cash flows needs. A larger allocation to intermediate-term compared to long-term bonds is preferred in order to match the maturity of these needs.

•

Real estate: A low allocation because his job income may be highly correlated with domestic real estate market, resulting in an otherwise high allocation to real estate once human capital is considered. Also, direct investment in real estate is illiquid, although there is no mention of whether it is directly or indirectly held.

•

Hedge funds: A low allocation because hedge funds of illiquidity given potential lock-up period provisions.

•

Given these considerations, the portfolio that is most suitable for Joe is Portfolio 5. [24 marks]

In a follow-up meeting with Sarah, Joe asks Sarah how she came up with the capital market expectations the asset classes. She explains that her hedge fund estimates were motivated by recent headline news that legendary hedge fund manager Day Ralio impressively outperformed the market for the fifth consecutive year. Sarah adds that US equities have outperformed International equities by about 2% points for the past three years and that she believes the trend will continue. She claims that she has always maintained the view that US bonds would underperform international bonds and that fixed income reports that land on her desk support that view; when Joe probes whether there were any reports with differing views, she replied, “None that were worth remembering!”.

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Page 5 of 7 Specimen Examination Paper

For domestic real estate, Sarah qualifies that her independent analysis revealed an expected return of 9% but, because most of her colleagues have much lower expectations, she decided to reduce her estimate so as to maintain credibility. Further, she used appraised as opposed to transacted values to estimate the standard deviation of real estate since there were insufficient real estate transactions. When Joe asks if there is a more robust way to determine an optimal portfolio for him, Sarah quips, “Yes, we can use standard mean-variance optimisation by Nobel laureate Harry Markowitz—the most robust technique currently available”.

Question 4 (a)

Critique Sarah’s approach to forming capital market expectations in terms of potential psychological pitfalls and other challenges in forecasting. (10 marks)

(b)

Evaluate Sarah’s claim that standard mean-variance optimisation is the most robust technique currently available. (6 marks)

Marking Guide: Suggested answer for Question 4(a): • • • • •

Potential recallability trap for her hedge fund estimate Potential status quo trap for her US versus international equity differential Potential confirming evidence trap for her US versus international bond differential Potential prudence trap for her domestic real estate return estimate Using appraised values for real estate instead of market price transaction data can cause its true standard deviation to be underestimated [10 marks]

Suggested answer for Question 4(b): • • •

Standard MVO suffers from asset allocations that are highly sensitive to changes in inputs, especially expected return Standard MVO also produces portfolio allocations that are concentrated in only a few asset classes, which are not intuitive Resampled efficient frontier or the Black-Litterman approach can result in portfolio allocations that are more diversified and stable over time [6 marks]

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Page 6 of 7 Specimen Examination Paper

After the second meeting, Joe decided that it may be better to invest with Sarah in stages instead. Joe opened an account with Sarah and placed an initial amount of $800,000 with Sarah at the beginning of the April. He then placed an additional amount of $200,000 with Sarah at end of day 20, at which point his account was valued at $1,050,000. By the end of April, Joe’s account was worth $1,300,000. Joe contacts Sarah at that point to find out how his portfolio had performed for the month.

Question 5 (a)

Calculate the portfolio’s time-weighted return for the month of April. (5 marks)

(b)

Joe also wonders about the portfolio’s money-weighted return and Sarah guesses that the effective (daily compounded) money-weighted for April is 30.88% or 34.88%. Using Sarah’s guesses, estimate the portfolio’s money-weighted return for the month of April. (5 marks)

(c)

Sarah is expecting strong performance in the second half of May and Joe to inject substantial capital around mid-May. If Sarah had a choice, would she prefer to present the time- or money-weighted return for May? Explain your answer. (4 marks)

Marking Guide: Suggested answer for Question 5: (a)

Subperiod return (0,20) = (1,050,000 – 200,000)/800,000 – 1 = 6.25% Subperiod return (20,30) = 1,300,000/1,050,000 – 1 = 23.81% Time-weighted return = (1 + 0.0625)(1 + 0.2381) – 1 = 31.55% [5 marks]

(b)

1,300,000 = 800,000(1 + r)30 + 200,000(1 + r)10 By trial and error, r = 0.010023 Money-weighted return = (1 + 0.010023)30 – 1 = 34.88% [5 marks]

(c)

If funds are contributed to an account prior to a period of strong performance, then the MWR will be positively affected compared to the TWR, as a relatively large sum is invested at a high growth rate. So Sarah may prefer to present the MWR in order to give a better impression of performance. [4 marks]

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