The difference is due mainly to rounding and the early-exercise potential of
the American put. In mathematical terms
The synthetic long stock is approximately equal to the long stock position
when considering the effect of interest. The two lines in Exhibit 6.7 —
representing stock and synthetic stock—would converge with each passing
day as the calculated interest decreases.
This equation works as well for a synthetic short stock position; reversing
the signs reveals the synthetic for short stock.
Or, in this case,
Shorting stock at $51.54 is about equal to selling the 50 call and buying
the 50 put for a $2 credit based on the interest of 0.486 computed on the 50
strike. Again, the $0.016 disparity between the calculated interest and the
actual difference between the synthetic value and the stock price is a
function of rounding and early exercise. More on this in the “Conversions
and Reversals” section.