Daycount and Frequency

Two market standards for US dollar interest rates are semi-annual compounding with 30/360 daycount (semi-bond, denoted y_SB), and annual compounding with act/360 daycount (annual-money, denoted y_AM).

(a) Derive an expression for y_AM in terms of y_SB . You can assume all years have 365 days.

(b) Show that when y_SB = 6%, AM for the cases y_SB = 5% and y_SB = 7% and use your answers to deduce which rate has larger standard deviation.

(c) The volatility of a rate y is usually defined as the standard deviation for its logarithm, and can be well approximated by . By differentiating your answer to (a), derive an expression for the ratio of the volatility of y_AM to the volatility of y_SB, assuming that he current level of rates is y_SB = 6%. Compare your answer to your empirical result from (b).

lys B yAMI lys B yAMI