Question 2 (a) You wish to invest in two risky securities with the following details Return for Security 1 Return for Security 2 Probability 15 12 0 2 19 14 0 3 21 10 0 3 25 20 0 2 The correlation coefficient ( 12 ) between returns of the two securities is 0 6 (i) Calculate the expected rate of return( r ) and risk( ) for the following portfolios 100 security 1 40 security 1 and 60 security 2 60 security 1 and 40 security 2 100 security 2 12 marks Explain how you could combine the risk free instrument and a risky portfolio with an expected return of 20 to obtain an expected return of 34 Assume the risk free rate of interest is 6 5 marks Suppose an insurance company has 350 million in capital available The gain from an investment portfolio of this bank during 12 month period is normally distributed with a mean of 70 million and a standard deviation rate of 160 million The insurance company considers 99 12 month value at risk ( 2 33) for setting its economic capital Assume the 1 tail of the loss distribution has the following values 0 6 probability corresponds to a 700 million loss and 0 4 probability corresponds to a 20 million loss Calculate annual risk adjusted return on capital (RAROC) of the investment portfolio, which considers the expected tail loss marks Suppose a project initially costs 900 million and generates cash flows of 350 million per year for three consecutive years Cash flows are realised at the end of each year The firm could decide to close down the project immediately after inception and would recover 800 million The firm could also choose to abandon the project and sell off assets at the beginning of year 2 and recover 700 million with 40 chance or 400 million with 60 chance The firm also could sell off assets at the beginning of year 3 and realise 300 million with 40 chance or 100 million with 60 chance Assume the discount rate is 5 Advise the firm whether and when it should exercise the option (i e abandon the project) and calculate the value of the option marks

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Question 2

(a) You wish to invest in two risky securities with the following details:

The correlation coefficient (₁₂) between returns of the two securities is -0.6.

(i) Calculate the expected rate of return(r) and risk() for the following portfolios:

[12 marks]

Explain how you could combine the risk-free instrument and a risky portfolio with an expected return of 20% to obtain an expected return of 34%. Assume the risk-free rate of interest is 6%.

[5 marks]

Suppose an insurance company has 350 million in capital available. The gain from an investment portfolio of this bank during 12-month period is normally distributed with a mean of 70 million and a standard deviation rate of 160 million. The insurance company considers 99% 12-month value at risk (=2.33) for setting its economic capital. Assume the 1% tail of the loss distribution has the following values: 0.6% probability corresponds to a 700 million loss and 0.4% probability corresponds to a 20 million loss. Calculate annual risk-adjusted return on capital (RAROC) of the investment portfolio, which considers the expected tail loss.
1. marks]
Suppose a project initially costs 900 million and generates cash flows of 350 million per year for three consecutive years. Cash flows are realised at the end of each year. The firm could decide to close down the project immediately after inception and would recover 800 million. The firm could also choose to abandon the project and sell off assets at the beginning of year 2 and recover 700 million with 40% chance or 400 million with 60% chance. The firm also could sell off assets at the beginning of year 3 and realise 300 million with 40% chance or 100 million with 60% chance. Assume the discount rate is 5%. Advise the firm whether and when it should exercise the option (i.e. abandon the project) and calculate the value of the option.
1. marks]