Question

6. Unlucky Louie has decided to try his cash management skills in other areas of investments. Louie notices that 1-year U.S. Treasury bills offer an annualized yield of 8 percent at the same time that an alternative 1-year investment offers a return of 10 percent (assume annual compounding).

   1. By how much would $100,000 grow in 1 year if invested in the U.S. Treasury bill?

   2. By how much would $100,000 grow in 1 year if invested in the alternative that offers a 10 percent return?

   3. Assume that the U.S. Treasury bill cannot default but that the alternative investment has a 97 percent chance of paying fully and a 3 percent chance of paying nothing. What is the expected cash flow from investing $100,000 in the alternative investment?

   4. What would be the expected cash flow from a third 1-year investment of $100,000 that offers a 90 percent chance of a 15 percent return, a 5 percent chance of paying back only 50 cents on each dollar invested, and a 5 percent chance of returning nothing?

Answer 1

Return from Treasury Bills = r_t = 8%

Value of $100000 in 1 year if invested in Treasury Bill = 100000*(1+r_t) = 100000*(1+0.08) = $108000

Return from Alternative Investment = r_a = 10%

Value of $100000 in 1 year if invested in Alternative Investment = 100000*(1+r_a) = 100000*(1+0.10) = $110000

Expected Return = Σ R_iP_i = 100000*0.97 + 0*0.03 = $97000

where, R_i is the return for Probability P_i

Expected Return = Σ R_iP_i = (100000*1.15)*0.90 + (100000*0.50)*0.05 + 0*0.05 = $106000