Stock-Options and Portfolio Management

Abstract

For many managers who have been granted them, stock-options represent a significant share of their wealth, in certain cases several times the value of other assets.

This tends to create a serious unbalance in the structure of their total portfolio, with an excessive exposure to their firm’s stock value, and also an excessive exposure to its volatility.

The result of that lack of diversification is that stock-options, unless hedged, may be worth less to the holder than their market, or model, value. The value loss may be quantified. With reasonable parameters for risk aversion, stock-options are worth to the holder 50 percent of their market value if that market value is equivalent to half the value of other assets, 30 percent if it is equivalent to the value of other assets, and 20 percent if it is equivalent to twice that value.

The loss is greater the higher the exercise price is: stock-options worth the equivalent of the other assets in market terms are worth to the holder 30 percent for options just at the money, 10 percent for a strike twice the share value, and 85 per cent for very low strikes which make options equivalent to the underlying stock.

The gap between market value and value to the holder also increases with stock volatility, whether it comes from a high beta or from a high specific volatility (the latter has a little more influence). It increases with the holder’s risk aversion.

Those findings certainly point to efficiency problems in the use of stock-options as a management tool. In addition, it is shown that the loss comes as well from the exposure to the stock’s volatility as from the exposure to the stock’s value.

This means that the mitigation of risk that could be expected, in the managed part of wealth, by reducing the exposure to (or even shorting) the risky assets, or better reducing the exposure to the firm’s stock, will be limited, except if the options are largely out of the money. However, a full coverage of options would conflict with their incentive objectives.

There is quite an important literature on stock-options and stock grants and their efficiency in terms of compensation tool, and on their tax treatment. This paper builds on that literature but focuses on a portfolio management issue.

Keywords: Stock Options, Portfolio management, Portfolio Optimization

JEL Classification: G11, G13, M52