Suppose a risk neutral agent has $100,000 today that he wants to save for one year. Compare the following three savings plans. Bank A offers a standard savings account with 4.3% p.a. (per annum). Bank B offers the following alternative: There is a basis interest rate of 1.2% p.a. and 40% participation on the performance of the S&P500. The maximum interest rate is capped at 10% p.a. (If the S&P increases by 4%, there is a bonus of 1.6% so that the total return is 2.8% p.a. If the return of the S&P is 30%, the plan has a total return of 10%. Note, if the S&P has a negative return, the interest rate remains at 1.2%.) Bank C offers the following alternative: There is a basis interest rate of 3% p.a. and 20% participation on the performance of the S&P500. The maximum interest rate is capped at 8% p.a. Suppose the S&P has 1000 points at t=0. At t=1 it can have {900, 990, 1000, 1020, 1030, 1040, 1100, 1200, 1300, 1400} points with equal probability. (a) Draw the payoff of alternative B as a function of the S&P (with the S&P performance on the X-axis, and the (total) return of the plan on the Y-axis.) (b) The agent maximizes the expected amount at t=1. Which plan is best? How much can the agent spend in expectation at t=1 if he chooses the best one?
Suppose a risk neutral agent has $100,000 today that he wants to save for one year. Compare
the following three savings plans.
Bank A offers a standard savings account with 4.3% p.a. (per annum).
Bank B offers the following alternative:
There is a basis interest rate of 1.2% p.a. and 40% participation on the performance of the
S&P500. The maximum interest rate is capped at 10% p.a. (If the S&P increases by 4%, there
is a bonus of 1.6% so that the total return is 2.8% p.a. If the return of the S&P is 30%, the plan
has a total return of 10%. Note, if the S&P has a negative return, the interest rate remains at
1.2%.)
Bank C offers the following alternative:
There is a basis interest rate of 3% p.a. and 20% participation on the performance of the
S&P500. The maximum interest rate is capped at 8% p.a.
Suppose the S&P has 1000 points at t=0. At t=1 it can have {900, 990, 1000, 1020, 1030,
1040, 1100, 1200, 1300, 1400} points with equal probability.
(a) Draw the payoff of alternative B as a function of the S&P (with the S&P performance
on the X-axis, and the (total) return of the plan on the Y-axis.)
(b) The agent maximizes the expected amount at t=1. Which plan is best? How much can
the agent spend in expectation at t=1 if he chooses the best one?
Here,
Details of Bank A:
Offers Fixed Interest Rate of 4.3% per annum
Details of Bank B:
Offers Basis interest rate of 1.2% p.a. and 40% participation on the performance of the S&P500. The maximum interest rate is capped at 10% p.a
Details of Bank C:
Offers Basis interest rate of 3% p.a. and 20% participation on the performance of the S&P500. The maximum interest rate is capped at 8% p.a.
Details of S&P :
The S&P has 1000 points at t=0. At t=1 it can have {900, 990, 1000, 1020, 1030,
1040, 1100, 1200, 1300, 1400} points with equal probability.
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