FM for Actuaries

140 CHAPTER 4
4.30 Mary sells short 200 shares of Conron and gives the broker the minimum
amount of $6,700 to establish the margin account. The initial margin requirement
is 50% and the margin deposit earns no interest.
(a) Find the price of the stock when Mary sells short.
(b) After 3 months, Mary covers the short position, resulting in a return
of −10%. The interest credited to the margin account in the 3-month
period is $50. Find the price of the stock when Mary covers the short
position.
4.31 You sold short 100 shares in Outel at $33 per share. After 4 months, the stock
paid $3 of dividend. After 2 more months you covered the short position by
purchasing the stock at a price of $26. If the initial margin requirement is
50%, the margin deposit earns $30 interest in the half-year period, and each
share incurs a transaction cost of $1 when you sold short the stock, find the
rate of return over the half-year period.
4.32 Suppose you sell short 100 shares of a stock for $50 per share and give your
broker 50% margin. The margin deposit earns no interest. When the stock
price decreases by 12%, you close the short position. Calculate the rate of
return if the stock pays a dividend of (a) $0.5 per share, (b) $1 per share, and
(c) $2 per share before you close the short position. What is the effect of the
dividend on the rate of return?
4.33 A fund credits interest according to the following table:
Portfolio
Calendar year Investment-year rates (%) rates (%)
of investment (Y ) i Y 1 i Y 2 i Y 3 i Y 4 i Y +4
2009 5.6 5.6 5.7 5.9 5.9
2010 5.6 5.6 5.7 5.9 5.8
2011 5.6 5.7 5.8 6.2 5.9
2012 5.8 5.9 6.0 6.3 X
2013 6.2 6.3 6.6 6.5
2014 6.7 6.4 6.8
2015 7.1 7.3
2016 Z