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 U=Sm2 where m and are the mean and standard deviation of S respectively for a particular investor and both investors use U to transform their spread distribution.

(a) (2 marks) In your own words, explain what is meant by rich-cheap analysis.

(b) (3 marks) 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) (3 marks) What risks are there in implementing rich-cheap analysis? How are these overcome in practice in the implementation of the strategy?