Question

In an ideal market the one-year spot rate is 6%, and the two year spot rate is 5%. a) A bank offers for a bank account starting one year in the future and ending two years in the future an interest rate of 3.5%. Explain an investment strategy that allows you to earn money without risk. b) Same as (a) but the bank offers an interest rate of 4.5%.

Answer 1

In ideal market:

1-year spot rate = 6%

2-year spot rate = 5%

Thus,

1-year forward rate starting in one year:

1.052 1.1] = 1.06 二

f1,1= 4.01%

(a) A bank is offering 1-year forward rate starting in one year of 3.5%, this forward rate is less than implied 1-year forward rate of ideal market. Thus, arbitrage opportunity exist here.

Investment Strategy:

Borrow from Bank(i.e offering lower 1-year forward rate) and Invest in ideal market for two years at 2-year spot rate.

Effective interest rate charged by bank in two years:

=(1.06 + 1.035) 1/2_1

= 4.74%

And, Interest rate earned in ideal market for two year investment = 5%

Thus, Risk free gain in terms of interest rate = 5.00%-4.74% = 0.26%

(b)

If A bank is offering 1-year forward rate starting in one year of 4.5%, this forward rate is more than implied 1-year forward rate of ideal market. Thus, arbitrage opportunity exist here.

Investment Strategy:

Invest in Bank(i.e offering higher 1-year forward rate) and borrow from ideal market for two years at 2-year spot rate.

Effective interest rate earned from bank in two years:

= (1.06 * 1.045) 1/2 - 1

= 5.25%

And, Interest rate charged by ideal market for two year borrowing = 5%

Thus, Risk free gain in terms of interest rate = 5.25%-5.00% = 0.25%

Hope this will help, please do comment if you need any further explanation. Your feedback would be highly appreciated.