Krzys’ Ostaszewski http://www.math.ilstu.edu/krzysio/ Exercise 21
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Society of Actuaries Sample Examination 140-82-96, Problem No. 19
Brian sells a stock short for 800 and buys it back one year later at a price of 805. The
required margin on the sale is 62.5% and interest is credited on the margin deposit at an
annual effective rate of i. Dividends of 15 are paid during the year. Brian’s yield rate over
the 1-year period is j. If the interest credited on the margin deposit had been 1.25i, with
everything else remaining the same, Brian’s yield rate over the 1-year period would have
been 1.5j. Calculate i.
A. 4%
B. 5%
C. 6%
D. 7%
E. 8%
Solution.
Brian’s margin deposit is 0.625 ! 800 = 500. He receives interest in the amount 500i. His
total net income is
!5 ) + 500i ! 15
(!
! = 500i ! 20.
dividend
= 800 ! 805
Therefore,
500i ! 20
= i ! 0.04.
500
If the interest credited on the margin deposit had been 1.25i, his total net income would
have been
( !5 ) + 500 "1.25i ! 15 = 625i ! 20.
His yield rate would have been then
625i ! 20
1.5 j =
= 1.25i ! 0.04.
500
These are two equations with two unknowns, and by substituting j = i ! 0.04 into the
second equation, we obtain
1.5 ( i ! 0.04 ) = 1.25i ! 0.04,
or
1.5i ! 1.25i = 0.06 ! 0.04,
and
0.02
i=
= 0.08 = 8.00%.
0.25
Answer E.
j=
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