Question

Market Price ($)	Cash Flow in One Year ($)
Security	Today	Poor Economy	Good Economy
A	450	800	0
B	300	0	800
C	???	4000	800

1. Calculate the no-arbitrage price for security C?
2. Calculate value of the risk free rate

Answer 1

1.
Security C can be constructed by buying 5 unit of Security A and 1 unit of Security B

Hence, Price of Security C=Price of 5 units of Security A+Price of 1 unit of Security B=450*5+300*1=2550.00

2.
Let risk free rate be p
Let probability of poor economy be p and probability of good economy be 1-p

From Security A: 800*p/(1+r)=450

From Security B: 800*(1-p)/(1+r)=300

Solving the two simultaneously, we get
p/(1-p)=450/300
=>1/p-1=300/450
=>1/p=300/450+1
=>p=1/(300/450+1)

and r=800/(300/450+1)*1/450-1=6.6667%