Question

What would be your implied (repo) rate on a stock index arbitrage, if the underlying index' log dividend yield is 5.9%, the log risk free rate is 2%, the underlying index' spot value is 52 and the price of one contract of 151-day futures is 2,773? One contract is equivalent to 50 times the underlying index' value. Provide your answer in percent, rounded to two digits, omitting the % sign.

Answer #1

Solution :

Dividend Yield = 5.9%, risk free rate rM = 2% , Fm= Future price = 2773, Spot price = 52 * 50= 2600

Time = 151 days,

So if we see the Fair price based on this information then

F =Fair Price = Spot * ( 1 + (rm- d)*151/365) = 2558.05

Here Fm > F so their is an arbitrage opportunity and after shorting at current price one can earn the profit

So it is a kind of repo

Implied repo =

= **9.96%**

Note: I have chosen 360 days convention and answer is 9.96%. If we chose 365 days then answer will be 10.18%

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