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Question 73 portfolio risk, standard deviation

Portfolio Details
Stock	Expected return	Standard deviation	Covariance ##(\sigma_{A,B})##	Beta	Dollars invested
A	0.2	0.4	0.12	0.5	40
B	0.3	0.8	0.12	1.5	80

What is the standard deviation (not variance) of the above portfolio? Note that the stocks' covariance is given, not correlation.

Question 219 profitability index

A project has the following cash flows:

Project Cash Flows
Time (yrs)	Cash flow ($)
0	-90
1	30
2	105

The required return of a project is 10%, given as an effective annual rate. Assume that the cash flows shown in the table are paid all at once at the given point in time.

What is the Profitability Index (PI) of the project?

Question 233 bond pricing

A four year bond has a face value of $100, a yield of 9% and a fixed coupon rate of 6%, paid semi-annually. What is its price?

Question 312 foreign exchange rate, American and European terms

If the current AUD exchange rate is USD 0.9686 = AUD 1, what is the American terms quote of the AUD against the USD?

Question 319 foreign exchange rate, monetary policy, American and European terms

Investors expect the Reserve Bank of Australia (RBA) to keep the policy rate steady at their next meeting.

Then unexpectedly, the RBA announce that they will increase the policy rate by 25 basis points due to fears that the economy is growing too fast and that inflation will be above their target rate of 2 to 3 per cent.

What do you expect to happen to Australia's exchange rate in the short term? The Australian dollar is likely to:

Question 394 real option, option

Question 431 option, no explanation

A European put option will mature in ##T## years with a strike price of ##K## dollars. The underlying asset has a price of ##S## dollars.

What is an expression for the payoff at maturity ##(f_T)## in dollars from having written (being short) the put option?

Question 439 option, no explanation

Question 718 arithmetic and geometric averages

The symbol ##\text{GDR}_{0\rightarrow 1}## represents a stock's gross discrete return per annum over the first year. ##\text{GDR}_{0\rightarrow 1} = P_1/P_0##. The subscript indicates the time period that the return is mentioned over. So for example, ##\text{AAGDR}_{1 \rightarrow 3}## is the arithmetic average GDR measured over the two year period from years 1 to 3, but it is expressed as a per annum rate.

Which of the below statements about the arithmetic and geometric average GDR is NOT correct?

(a) Arithmetic average gross discrete return is ##\text{AAGDR}_{0\rightarrow T} = \dfrac{\text{GDR}_{0 \rightarrow 1}+\text{GDR}_{1\rightarrow 2}+...+\text{GDR}_{T-1 \rightarrow T}}{T}##

(b) Geometric average gross discrete return is ##\text{GAGDR}_{0\rightarrow T} = \dfrac{\text{GDR}_{0 \rightarrow 1} . \text{GDR}_{1\rightarrow 2} ... \text{GDR}_{T-1 \rightarrow T}}{T}##

(c) The geometric average gross discrete return can be quickly found using the first ##(P_0)## and last ##(P_T)## prices. ##\text{GAGDR}_{0\rightarrow T} = \left( \dfrac{P_T}{P_0} \right)^{1/T}##

(d) The arithmetic average is always bigger than or equal to the geometric average, ##\text{AAGDR} \ge \text{GAGDR}##.

(e) The arithmetic and geometric averages of returns will be equal if the variance of the stock's returns is zero.

Question 904 option, Black-Scholes-Merton option pricing, option on future on stock index

A six month European-style call option on six month S&P500 index futures has a strike price of 2800 points.

The six month futures price on the S&P500 index is currently at 2740.805274 points. The futures underlie the call option.

The S&P500 stock index currently trades at 2700 points. The stock index underlies the futures. The stock index's standard deviation of continuously compounded returns is 25% pa.

The risk-free interest rate is 5% pa continuously compounded.

Use the Black-Scholes-Merton formula to calculate the option price. The call option price now is: