STOCHASTIC

PORTFOLIO CHOICE AND THE KELLY CRITERION
Fig. 2. Price history of Kaufman and Broad common S versus the warrants W. The
points moved up and to the right until they reached the neighborhood of (38, 17). At this
point a 3 :2 hedge (15,000 warrants long, 11,200 common short) was instituted. As the points
continued to move up and to the right during the next few months, the position was closed
but in stages with the final liquidation at about (58, 36). Terms of warrant: one warrant plus
$21.67 -+ one share common stock until 3-1-74. Full protection against dilution. The company
has the right to reduce the exercise price for temporary periods; 750,000 warrants and
5,940,000 common outstanding. Common dividends Q.05ex 10-26-70.
replace this in our illustrative analysis by W = 0.5S if S f£ 44 and W = S-22
if S ^ 44. The lines are also indicated in Fig. 2.
Past history at the time the hedge was instituted in late 1970 supported
the fit for S ^ 38. The conversion feature of the warrant ensures W ^ S — 21.67
until the warrant expires. Thus W = 5 — 21.67 for S 2i 44 underestimates the
price of the warrant in this region. Extensive historical studies of warrants
[12, 13, 24, 27] show that the past history fit would probably be maintained
until about two years before expiration, i.e., until about March 1972. Thus
4. THE CAPITAL GROWTH CRITERION AND CONTINUOUS-TIME MODELS 613