Question

Consider two securities that pay risk-free cash flows over the next two years and that have the current market prices shown here:

Security	Price Today ($)	Cash Flow in One Year ($)	Cash Flow in Two Years ($)
B1	94	100	0
B2	85	0	100

1. What is the no-arbitrage price of a security that pays cash flows of $100 in one year and $100 in two years?      
2. What is the no-arbitrage price of a security that pays cash flows of $100 in one year and $500 in two years?
3. Suppose a security with cash flows of $50 in one year and $100 in two years is trading for a price of $130. What arbitrage opportunity is available?

Answer 1

No abritage price are the price of security which have same price as market without adding any opportunity risk for future profit to it.

a. In given first case , if we see the security B1 is giving cash flow in year 1 of $100 and in second year it is giving 0 cash flow hence security B1 alone cannot be consider , same for B2 is giving 0 cashflow in year one and 100 in year 2 , hence both the security is to be consider as portfolio

Hence No abritage price = $94 +$85 = $179

b. As we know B1 only give profit in year one , so we have to take into portfoli B2 also , but in year two cashflow required is 500, hence 1 unit of B1 and 5 unit of B2 security is to be purchase

No Abritage price =$94 +(5×85)=$519

c.New security price is $130 ,

and if we consider portflio price of two giving same cash flow

security B1 and B2 =1/2 of B1 + B2 =94/2+85 = 132

As the No abritage price is higher than the Abritage there is abritage opportunit ie profit

One should by two unit of this security at $130 =130×2 =260

And sell one unit of B1 and 2 unit of B2 getting total =1×94+2×85 = 264

Giving Abritage Gain =($264-260) =$4

hence abritage opportunity exists which will give profit of $4