Behavioral aspects of the design and marketing of financial products - Security Design Special Issue

Financial Management (Financial Management Association), Summer, 1993 by Hersh Shefrin, Meir Statman

v(1.67) |is greater than~ 1/2|v(20) - v(15)~

or in another form

v(1.67) 1/2v(15) |is greater than~ 1/2v(20). (3)

The prospect theory expected value of the covered call position exceeds the prospect theory expected value of the stock-only position for investors who are sufficiently risk-averse in the domain of gains.

Exhibit 2. A Glossary of Abbreviations

s         = Stock-only position.
cc        = Covered call position.
pcc-1     = Partially covered call position in the first frame.
pcc-2     = Partially covered call position in the second
            frame.
fcc       = Fully covered call position.
fcc-out   = Covered call position with out-of-the-money calls.
fcc-in    = Covered call position with in-the-money calls.
ccss      = Covered call position where the stock is sold when
            the call is in-the-money at expiration.
ccr       = Covered call position where the call is repurchased
            when the call is in-the-money at expiration.

The above comparison is useful because brokers and investors often compare covered calls to stock-only positions. However, the comparison confounds the effect of framing with the effect of attitudes toward risk. The covered call and stock-only positions differ not only in their prospect theory expected values but also in their underlying cash flows. In particular, a covered call position is less risky than a stock-only position. Thus, one might reasonably argue that covered calls are preferred to stock-only positions because of their lower risk rather than because of their prospect theory properties.

To disentangle framing effects from the effects of attitudes toward risk, we compare covered calls to alternatives with identical cash flows. The covered call position in our example required an initial cash outflow of $18.33 composed of $20 paid for a share of Alpha and $1.67 received for a call on Alpha. The total gain is $16.67 in the up state and the total loss is $8.33 in the down state.

While it is conceivable that standard investors who are sufficiently risk-averse might prefer covered calls over stock-only positions, there is no apparent reason that might lead standard investors to prefer covered calls with out-of-the-money calls over covered calls with in-the-money calls; to prefer fully covered calls over partially covered calls; or to frame covered calls as having a gain on the stock rather than a loss on the option. We suggest that all these preferences are consistent with the preferences of prospect theory investors.

B. A Comparison of a Fully Covered to a Partially Covered Call Position

The Louis Harris Survey |23~ revealed that most covered call positions are structured as fully covered positions. Compare a fully covered call position consisting of buying one share of Alpha and selling one call on Alpha to a partially covered position consisting of buying 1.25 shares of Alpha and selling 2.5 calls on Alpha. The initial cash outlay for the partially covered call position, $18.33, is identical to the initial cash outlay for the fully covered call position. Also, the net gain in either position in the up state is $16.67 and the net loss in either position in the down state is $8.33.