# Arbitrage Possible?

Jorgen Welsher, CFA obtains the following quotes for zero coupon government bonds all with a par value of \$100.

Type of Price Delivery (years) Maturity (years) Price
Spot 0 3 \$91.51
Forward 2 3 \$94.55
Spot 0 2 \$92.45

Welsher can earn arbitrage profits by:

A)

buying the 2-year bond in the spot market, going long the forward contract and selling the 3-year bond in the spot market.

B)

selling the 2-year bond in the spot market, going short the forward contract and buying the 3-year bond in the spot market.

C)

buying the 2-year bond in the spot market, going short the forward contract and selling the 3-year bond in the spot market.

I got the correct answer but maybe it was coincidence? This is how I solved it.

If you buy/go long you get the appreciation from the purchase price up to par so:
Spot 2 year: (\$100 - \$92.45) = \$7.55
Forward 3 year: (\$100 - \$94.55) = \$5.45
Short Spot 3 year (you owe the difference: (\$100 - \$91.51) = \$8.49

\$7.55 + \$5.45 - *\$8.49 = \$4.51 in arbitrage profit?

A 3 year zero coupon is equivalent to a 2 year spot followed by reinvesting in the forward. The 3 year spot is selling for 91.51; the 2 year + forward combo has a market price of 87.411 (100 * 0.9455 * 0.9245). So the 3 year zero is overvalued.