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

E|v(fcc-out)~ = v($1.67) 1/2|v($15) v(-$10)~. (7)

The prospect theory expected value of the covered call with in-the-money call (fcc-in) is

E|v(fcc-in)~ = v($41.67) 1/2|v($25) v(-$50)~. (8)

The covered call with an out-of-the-money call is preferred over the covered call with an in-the-money call for investors who exhibit sufficiently high risk-aversion in the domain of gains and sufficiently high risk-seeking in the domain of losses.

TABULAR DATA OMITTED

D. A Comparison of Repurchasing Calls and Selling Stock

Do holders of covered calls prefer to frame their positions as selling their shares when the calls are about to be exercised, thereby realizing a gain on the stock, or do they prefer to frame their positions as repurchasing the calls, thereby realizing a loss on the calls? The structure of Gross's |14~ sales pitch implies that the stock is sold. The gains and losses associated

with the two alternative frames are presented in Exhibit 5. Note, again, that the net cash flows of the covered call in the two frames are identical.

The prospect theory expected value of a covered call where the stock is sold (ccss) is:

E|v(ccss)~ = v(1.67) 1/2|v(15) v(-10)~. (9)

The prospect theory expected value of a covered call where the call is repurchased (ccr) is:

E|v(ccr)~ = 1/2|v(-3.33) v(1.67)~ 1/2|v(20) v(-10)~. (10)

The shape of the value function indicates that the prospect theory expected value of a covered call when the stock is sold exceeds the prospect theory expected value of a covered call when the call is repurchased for investors who are sufficiently risk-averse in the domain of gains. It appears that the selling frame masks the loss sustained on the option.

E. Hypotheses

We offer three hypotheses:

(i) More covered call positions are formed with out-of-the-money calls than with in-the-money calls.

(ii) More covered call positions are fully covered than partially covered.

(iii) Relative to the prescriptions of standard finance, investors with covered call positions are reluctant to repurchase the call when the purchase entails tthe realization of a loss.(8)

Exhibit 5. The Framing of a Covered Call Where the Stock is
Sold and Where the Option is Repurchased

                         Up State           Down State
Mental              Stock      Option
Subaccounts         Sold     Repurchased

Capital gains on    $15.00     $20.00         -$10.00
the share

Gain on the call     $1.67     -$3.33           $1.67

Total               $16.67     $16.67          -$8.33

IV. Covered Calls and the Behavioral Life Cycle Theory

Recall that Gross |14~ frames the cash flows of a covered call into three mental accounts: dividends, option premium and the increase in the price of the stock to the option exercise price. The first two accounts can be labeled as "downside protected" or "bird-in-the-hand" accounts, while the third can be labeled as an "upside potential" account. Gross describes the writing of a covered call as a transfer from an upside potential account (i.e., "unknown, unknowable profit possibility") into a bird-in-the-hand account (i.e., money "paid to you right away, on the very next business day -- money that is yours to keep forever").