Daycount and frequency Two market standards for US dollar interest rates are semi-annual compounding with 30/360 daycount (semi-bond, denoted ySB), and annual compounding with act/360 daycount (annual-money, denoted yAM)
(a) Derive an expression for yAM in terms of ySB. You can assume all years have 365 days.
(b) Show that when ySB = 6%, | ySB - yAM |AM for the cases ySB = 5% and ySB = 7% and use your answers to deduce which rate has larger standard deviation.
(c) The volatility of a rate yis usually defined as the standard deviation of its logarithm, and can be well approximated by 
. By differentiating your answer to (a), derive an expression for the ratio of the volatility of yAM to the volatility of ySB, assuming that the current level of rates is ySB = 6%. Compare your answer to your empirical result from (b).