Question

1.Security’s market price is $500, risk-free rate is 5%. The security makes one risk-free payment in one year and matures. What must be risk-free payoff if the security in one year to make you interested in investing in this security?

2.Risk-free investment pays $550 in two years, risk-free interest rate is 5%. What is the highest amount you would agree to pay for this security

Answer 1

(1) The risk-free payoff in one year, when discounted at the risk-free rate should equal the the current security market price so as to conform to the principles of time value of money and avoid abritrage.

Let the payoff be $ P, CurrenT price = $ 500 and Risk-Free Rate = 5 %

Therefore, 500 = P / 1.05

P = $ 525

(2) The risk-free payoff worth $ 550 after two years, when discounted at the risk-free rate of 5 % should equal the the current security market price so as to conform to the principles of time value of money and avoid abritrage.

Let the current market price be $ K

Therefore, K = 550 / (1.05)^(2) ~ $ 498.87