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1.whether the following statement is true or false. According to the semi-strong efficient market hypothesis (EMH), a trading algorithm that has been profitable a year ago has 100% probability of being successful in the following year. Select one: O True O False
2.Design an Excel financial model that can help to answer the following parts (part 1 - 3). 5 marks will be allocated for the presentation and clarity of your model (e.g., if there are clear headings, clear arrangement for input cells, appropriate use of colors, have some degree of flexibility, generate warning messages for wrong user inputs, etc.).
Part 1 (8 marks)
Suppose you receive $100 at the end of each year for the next three years.
a. (2 marks)
If the interest rate is 8% per annum (interest paid annually), what is the present value of these cash flows?
b. (2 marks)
What is the future value in three years of the present value you computed in part (a)?
c. (2 marks)
Assume that no withdrawals are made from the savings account until the end of the third year. What is the interest component?
d. (2 marks)
Compute the effective 3 years rate (total interest over 3 years). Hint: EFFECT function is not appropriate for this part as it is often used to compute an effective annual interest rate from a nominal interest rate.
Part 2 (6 marks)
Your uncle has just announced that he is going to give you $15,000 per year at the end of each of the next 4 years.
a. (2 marks)
If the relevant interest rate is 7%, what is the value today of this promise?
b. (2 marks)
If the interest rate changes to 8%, what is the value today of this promise?
c. (2 marks)
Explain how interest rates influence the value of the promise in parts (a) and (b).
Part 3 (6 marks)
Peter borrowed $800,000 to refit his fishing trawler. The loan requires monthly repayments over 15 years. When he borrowed the money the interest rate was 13.5% per annum, but 18 months later the bank increased the interest rate to 15% per annum, in line with market rates. The bank tells Peter he can increase his monthly repayment (so as to pay off the loan by the originally agreed date) or he can extend the term of loan (and keep making the same monthly repayment). Calculate:
a. (4 marks)
The new monthly repayment if Peter accepts the first option.
b. (2 marks)
The extra period added to the loan term if Peter accepts the second option.
3.Suppose that the current exchange rate is SF1.25/$ and three month forward exchange rate is SF1.30/$. The three-month interest rate is 4 percent per annum in United States and 8 percent per annum in Switzerland. Assume that you can borrow up to $1,000,000 or SF 1,250,000.
a) Is Interest Rate Parity holding?
b) If your answer to part a is no, how would you realize a certain profit via a covered interest arbitrage? Also determine the size of the arbitrage profit.
1.Efficient Market Hypothesis (EMH) is a hypothesis which states that the traded share price reflect the true value of the shares and it reflects all the information. According to EMH, the shares/stocks always trade at their true fair value so investors can neither buy an underpriced stock or sell stocks at inflated price.
There are three variations of EMH -
1) Weak Efficient Market Hypothesis
2) Semi-strong Efficient Market Hypothesis
3) Strong Efficient Market Hypothesis.
Since the question is on Semi-strong EMH, lets focus on the same.
Semi-strong Efficient Market Hypothesis, is the variation of EMH which states that the current stock prices adjusts quickly to any new information available about the stock. The Semi-strog EMH proposes that fundamental and technical analysis are not useful in predicting stock's future price movement.
Based on the above, the statement that according to Semi-strong EMH, a trading algorithm that has been profitable a year ago has 100% probability of being successfl the following year is False
2.$100 at end of each year , Interest rate is 8% ,
PV = PV1 + PV2 + PV3
Pv1 = 100/(1+.08)
PV2 = 100/(1+.08)^2
PV3 =100/(1+.08)^3
PV = PV1 + PV2 + PV3 = 257.71
EXCEL function = PV(rate, nper,pmt,[fv],[type]) , rate = interest rate per period , nper = no.of payment periods, pmt= payment per each period, [fv] = future value you want to attain , by default it is zero, [type]= payment at the beginning=1; payment at the end of the period=0 or omitted
FUTURE VALUE = PV(1.08)^3 = 324.6404
FV=FV1+FV2+FV3
=FV(rate, nper,pmt,[pv],[type]) ,rate = interest rate per period , nper = no.of payment periods, pmt= payment per each period, [fv] = future value you want to attain , by default it is zero, [type]= payment at the beginning=1; payment at the end of the period=0 or omitted
100(1.08)^2+100(1.08)+100 = 324.64, interest component = 24.64
Please comment if you want any clarification
3.
If interest rate parity held true then the three month forward exchange rate should be = Spot rate x (1 + n/12 x iSF) / (1 + n/12 x iUS) = 1.25 x (1 + 3/12 x 8%) / (1 + 3/12 x 4%) = SF 1.26 / $
However the actual forward rate is SF 1.30 / $
Hence, the interest rate parity is not holding true.
Part (b)
Arbitrage strategy:
Arbitrage profit = 1,313,000 - 1,275,000 = SF 38,000
