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# You have £1000 and you would like to invest £700 into asset A and £300 into asset B. Compute the expected return of your portfolio (call it AB) and its standard deviation.

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Section 1 – Answer one out of two questions
Question 1
An economy has only two risky assets: asset A and asset B. Asset A represents the
stocks of Netflix, B the stocks of Amazon, respectively. Both assets pay uncertain rates
of return expected returns and standard deviations as follows:
E(rA) = 6%, E(rB) = 18%,
σ(rA) = 12%, σ(rB) = 21%,
Further the correlation coefficient between the returns on these two assets is –0.4.
(a)
You have £1000 and you would like to invest £700 into asset A and £300 into asset B.
Compute the expected return of your portfolio (call it AB) and its standard deviation.
Would you prefer to invest into this portfolio or into a single asset A or B? Justify your
answer.
(30 marks)
(b)
Suppose that there is one more asset available in the economy, asset C that represents
the stocks of Youtube. The expected return on this asset is 26%, its standard deviation
is 24% and the asset is not correlated to portfolio AB that you received in (a). You now
have additional £500 and you would like to diversify further your portfolio thus decide to
invest all the amount into asset C so that in the end you have a portfolio of three assets:
A, B and C. Compute the expected return of the new portfolio and its standard deviation.
You should also comment on the diversification abilities of asset C with respect to your
portfolio AB and discuss the limits of the diversification.
(40 marks)
(c)
Explain thoroughly the difference between beta as a measure of risk and variance as a
measure of risk.
(30 marks)
(Total 100 marks)
Question 2
(a)
(i) Suppose the expected returns and standard deviations of A and B are as
follows: 𝐸𝐸(𝑅𝑅𝐴𝐴) = 0.15; 𝐸𝐸(𝑅𝑅𝐵𝐵) = 0.25; 𝜎𝜎𝐴𝐴 = 0.40; 𝜎𝜎𝐵𝐵 = 0.65, respectively.
(ii) Calculate the expected return and standard deviation of a portfolio that is
composed of 40% A and 60% B when the correlation between returns on A
and B is 0.5.
(30 Marks)
(b)
Calculate the expected return and standard deviation of a portfolio that is composed of
40% A and 60% B when the correlation between returns on A and B is -0.5.
(40 Marks)
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(c)
You have £10,000 to invest in an equity portfolio. Your choices are Equity X with an
expected return of 14 per cent and Equity Y with an expected return of 10.5 per cent. If
your goal is to create a portfolio with an expected return of 12.4 per cent, how much
money will you invest in Equity X? In Equity Y?
(30 Marks)
(Total 100 marks)
Statistical formulas
Expected returns, two-asset portfolio: R aR a R pA B = +− (1 )
Portfolio Variance formula: 22 2 2 ( ) (1 ) 2 (1 )cov( , ) Var a a a a R R σσ σ P A = +− + − B A B
Covariance: {( )( ) } 1
(,)
n
AB A A B B i
i
Cov R R R R R R ρ =
=−− ∑
Correlation coefficient: (,) A B
AB
A B
Cov R R R
σ σ =
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Section 2 – Answer one out of two questions
Question 3
(a)
You are considering a project that could either be undertaken immediately or, in one
year. If undertaken immediately, the project costs £200 and has future cash flows of
£42 per year forever. If undertaken next year, it will cost £240 because of inflation and
the cash flows will be £48 per year forever.
If these are the only two relevant options (invest into the project now or in one year) and
the appropriate discount rate for this project is fixed at the level of 6% per annum, what
should be done? What is the pure value of the option to wait?
(30 marks)
(b)
Consider the case as in (3a) but now the appropriate discount rate is 12% per annum.
How does this influence your answer to the value of the option to wait?
(30 marks)
(c)
Briefly explain why Discounted Cash Flow (DCF) method cannot be used for valuing
options.
(20 marks)
(d)
Outline exactly what an abandonment option and a timing option are. Your discussion
should highlight the characteristics of these real options and you should provide an
overview as to how they can contribute to the investment opportunities for companies.
(20 marks)
(Total 100 marks)
Question 4
Suppose you currently observe the following term structure of interest rates (annualized
rates): r1 = 2%, r2 = 4%, r3 = 8%, r4 = 10%, r5 = 13%, r6 = 15%. Notation: ri stands for iyear interest rate. Given the above information:
(a)
Find the prices of the following two bonds: (i) two-year bond with coupon rate 5% and
face value \$1000 (paying coupons annually) and (ii) four-year bond with coupon rate
8% and with face value \$1000 (paying coupons annually) and justify the methodology
you use for finding the prices of these bonds. Do these bonds sell at a discount or a
premium? Give reasons to your answer.
(30 marks)
(b)
Explain what the yield to maturity on a bond is and how you would find it. For the fouryear and two-year bonds from (a) guess the magnitude of their yields (no need to
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calculate the yields!) and give reasons to your guess.
(30 marks)
(c)
Explain carefully the type of risk that investors face when investing in government bonds
and how this risk is related to the upward-sloping term structure of interest rates.
(40 marks)
(Total 100%)