A $100 face value one-year risk-free discount bond is priced at $95. The two-year discount bond is priced at $90. After one year, the two-year bond will take one of three equiprobable prices, spaced $5 apart. The middle value of these possible prices is
A) $90.25
B) $94.75
C) $95.00
D) $100.00

Question

A $100 face value one-year risk-free discount bond is priced at $95. The two-year discount bond is priced at $90. After one year, the two-year bond will take one of three equiprobable prices, spaced $5 apart. The middle value of these possible prices is 
A) $90.25
B) $94.75
C) $95.00
D) $100.00

Quizplus · Accepted Answer

The one-year risk-free discount bond is priced at $95, which means it has a yield of (100-95)/100 = 5%.

The two-year discount bond is priced at $90, which means it has a yield of (100-90)/100 = 10%.

After one year, the two-year bond will take one of three equiprobable prices, spaced $5 apart. The middle value of these possible prices is therefore (90+95+100)/3 = $95.

If we assume that the yields of the three possible prices are the same, then the expected yield after one year would be (95-90)/90 = 5.56%, which is greater than the yield of the one-year risk-free bond.

Therefore, it would be better to choose the two-year bond, even though there is some risk involved. The best choice is Option B, which gives the middle value of the possible prices of the two-year bond after one year.

A $100 Face Value One-Year Risk-Free Discount Bond Is Priced