Question 10

Suppose that an investor (denoted "Investor 1") calculates the spread of a particular bond, S, based on the past 300 trading days, to be distributed normally with a mean of 0.03% and a standard deviation of 0.04%.Note that the spread of a bond on a particular day is defined to be S = M - T where M is the yield to maturity used by the market on that day and T is the yield to maturity the investor believes should be used to price the bond on that day.

Now suppose that another investor (denoted "Investor 2") attempts to use rich-cheap analysis to price the same bond.This investor calculates the spread, based on the past 300 trading days, to be distributed normally with a mean of -0.02% (note that this is a negative number) and a standard deviation of 0.03%.

Also we define LaTeX: U=\frac{S-m}{2\sigma}U = S m 2 where LaTeX: mmand LaTeX: \sigma are the mean and standard deviation of S respectively for a particular investor and both investors use U to transform their spread distribution.

(a) In your own wrds, explain what is meant by rich-cheap analysis.

(b) Suppose that on a given day, the yield to maturity of a bond, based on observed bond prices, is 5% pa nominal.Investor 1 believes the yield to maturity for this bond on this day should be 4.88% (using their valuation model) while Investor 2 believes the yield to maturity for this bond should be 5.06%.

By performing appropriate calculations, calculate whether investor 1 would trade with investor 2.

HINT: For each investor, calculate when they would buy or sell the bond based on their own individual spread distribution.

(c)What risks are there in implementing rich-cheap analysis?How are these overcome in practice in the implementation of the strategy?