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US interest rates are currently 5.9% on one year T-bills. Assume that the American dollar is...

US interest rates are currently 5.9% on one year T-bills. Assume that the American dollar is quoted at 1 USD for $1.37 CDN and Canadian one year T-bills are 4.85%. If the forward spot rate is $1.42 what would the arbitrage be in Canadian dollar terms?

Solutions

Expert Solution

Risk free intrest rate in usa = 5.9%

Risk free interest rate in Canada =4.85%

Spot rate =1.37cnd/usd

If forword rate =1.42cnd /usd

Is there arbitrage opportunity ?

Theoretical forward rate for a/b

=F/s=1+ia/1+ib

F/1.37=1+.0485/1+.059

F= 1.37*(1.0485)/1.059

=1.356

So forword rate should be 1.356 cnd /$ but

Actually it is 1.42cnd/$ .so yes there is arbitrage opportunity exists.

Theoretically us doller should be at discount but actually it is at primium so we should borrow in canada and invest in usa

Arbitrage process

Today I borrow 137000cnd @4.85%

Convert it to $ @1.37cnd /$(us) so I will get 100000us$

Now deposit 100000usd in us @ 5.9%

After a year I will get 100000+ 5900$ (interest)

Sell 105900 $ @ 1.42 cnd/$ I will get (105900)= 150378 cnd

Initially I borrow 137000 cnd @4.85 % so interest on that amount becomes 6644.5cnd

Total payable to bank =137000+6644.5

=143644.5cnd

Arbitrage gain =150378-143644.5cnd

Net arbitrage gain =6733.5 cnd

jeff jeffy answered 2 years ago
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