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Section A
Answer ONE question from Section A, ONE question from Section B, and ONE other question.
You must show all your workings in quantitative answers.
Question 1. Answer ALL parts.
(a) The table presents the October 2018 performance of some major stock market indices and gold.
Monthly performance in October 2018
Arithmetic returns, %
S&P500 index
-6.9
Euro Stoxx 600 index
-5.6
CSI 300 index
-8.3
Topix index
-9.4
Gold
1.9
Answer: (Purchase past paper to get the full solution)
i). The formula which was used to calculate this arithmetic return data is £x/n. Just to take the ignores the compounding effect and order of returns and it is misleading when the investment returns are volatile. For small returns, arithmetic and logarithmic returns will be similar, but, as returns get further away from zero, these two formulations will produce increasingly different answers.
ii). Arithmetic returns aggregate well across portfolios. The arithmetic return for portfolio is simply equal to the weighted average of each constituents\’s arithmetic return. You might want to evaluate a portfolio of investments that might include similar investments (for example, all stocks or all bonds) or a combination of investments (for example, stocks, bonds and real estate). In this instance, you would calculate the mean rate of returns for this portfolio of investments for an individual year or for a number of years.
(b) An investment advisor has selected three equity funds as her current recommendations to a client. The expected returns, standard deviations and correlation coefficients for the three funds are:
Fund name
Expected returns, %
Standard deviation, %
Correlate with
Uk Alpha
European Growth
Asia-Pacific Value
UK Alpha
11
19
n.a.
0.34
0.82
20
26
0.08
14
21
The investment advisor has also recommended that the client's decision should involve selecting the optimal equally-weighted portfolio containing two of these three funds (i.e. 50%-50% weights).
[Total: 100 marks]
i). Calculate the expected risk:
We know that:
= (S.D alpha)2 (Weight alpha)2 + (S.D European)2(W European)2 + (S.D Asia)2 (W Asia)2 +2 (W alpha)(W European) r *Alpha*European (S.D Alpha) (S.D European) +2 (W European) (W Asia) r *European *Asia (S.D European) (S.D Asia) +2 (W Alpha) (W European) r *Alpha *Asia (S.D Alpha) (S.D Asia)
= (19)2(0.50)2 + (26)2(0.50)2 +(21)2(0.50)2 +2 (0.50)(0.50) 0.34(19)(26) +2(0.50)(0.50) 0.82(26)(21) +2(0.50)(0.50) 0.08(19)(21)
= 120.34 (taking the under root of this figure to find out the standard deviation or risk)
=10.96%
Expected return
= W Alpha * R Alpha + W European * R European + W Asia *R Asia
= 0.50*0.11 + 0.50*0.20 + 0.50*0.14
= 0.055 + 0.1 + 0.07
= 22.5%
ii). One of the three portfolios, the portfolio of UK and Asia pacific is the most attractive one because we know that the concept of high risk and high return. So, this portfolio has high risk and high return and same as low risk and low return. Some of the investors or clients are risk averse and some are aggressive, so the other two portfolios have different risk and return which is not a good portfolio for an investor to invest in it and through diversification, we can reduce the risk of the business and positive correlation also plays an important role to evaluate these portfolios and the correlation is also less than 1 in all portfolios.
iii). If the client has not imposed any restriction on portfolio choice, they he choose any portfolio out of these three portfolios and this is valid advice from advisor’s point of view, because he looks up the portfolio very carefully and managed it and most important to concern about the risk and return of that portfolio. We knew that under the assumption of homogeneous expectations, expected portfolio returns, is a linear function of portfolio risk. In practice, many investors and portfolio managers believe that estimates of security values are correct and market prices are incorrect. Such investors will not use the weights of the market portfolio but will never invest more than the market weights in securities that they believe are undervalued and less than the market weights in securities which they believe are overvalued.
Section B
Question 2. Answer ALL parts.
a. Explain the relevance of 'risk aversion' and 'efficient portfolios' for the capital market line (CML) of the capital asset pricing model (CAPM). [15 marks]
b. Using diagrams, explain the similarities and differences between the CML and the security market line (SML).[15 marks]
c. This table presents the annual expected returns and standard deviations for three stocks and for the market index. The risk free interest rate is 2%
Expected Return
Standard Deviation
Xavier plc
8%
9%
Yello plc
14%
15%
Zebra plc
19%
21%
Market index
16%
d). Classify the following scenarios according to systematic and unsystematic risk:
State your assumptions and explain your reasoning.[15 marks]
Question 3. Answer ALL parts.
a. An investor obtains the following Beta values for a set of companies. This is based on the capital asset pricing model (CAPM).
Company
Beta
Aron plc
0.1
Evon JSC
1.6
Brynie SA
0.5
Fled SA de CV
1.3
CARW nv
-0.2
Ghia LLC
0.4
Deiva AG
1.1
Hyppia SpA
0.8
The risk free asset (Rf) offers a 2% return.
b. The 'UK Infinity' index-tracking fund is considered to be a proxy for the 'market portfolio' of the CAPM. This fund has an expected return of 12% for the next year, and shares in the fund are currently priced at E30.
Jeremy plc has an estimated CAPM Beta value of 1.7 and its shares may be purchased for 330. This stock has an expected return of 24% for the next year.
A one-year risk-free asset may be purchased at e10.50 and offers a 3% return for the next year.
Question 4, Answer ALL parts.
a. Explain the relative merits of using an exchange-traded derivative contract versus using an over-the-counter derivative contract. [40 marks]
b. Explain the key characteristics of trading in the foreign exchange market, according to the BIS (Bank for International Settlements) surveys.[30 marks]
c. A fund manager recently made the following statements: "Company profits are mostly in line with expectations. Unemployment and inflation are low in many developed countries. Investors are concerned with global trade disputes. Global growth is slowing and interest rate rises are expected in the near future."
Explain how this statement can relate to the characteristics of 'factor models' of asset pricing and explain the main features of one model of this type.
[30 marks]
Question 5. Answer ALL parts.
(a)
Forward buyer: SI - F
Call option buyer: Max (SI - X, 0)
Put option buyer: Max (X - SI, 0)
Using diagrams and examples, explain the above three statements and identify the key differences among them.
[40 marks]
(b) Using the case of forward contracts, explain the relevance of arbitrage (or 'no arbitrage') in derivatives pricing.
(c) Using a numerical example, illustrate the use of stock index futures for hedging an underlying equity portfolio.
Question 6. Answer ALL parts.
(a) A legendary international investor recently announced that he will advise his widow to invest 90% of his wealth in a fund which tracks the W&P500 index. Critically analyse the potential theoretical and empirical justifications for this viewpoint.
(b) Critically analyse three examples of international stock market anomalies.
(c) Discuss the potential implications of each of the following hypothetical scenarios in the context of informational efficiency. State any assumptions that you make and comment on what further details you would seek in practice.
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Last updated: Oct 03, 2019 02:40 PM
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