Restricted Stocks and Options — Not as Restricted as We Thought ? … If there is no trading restriction and if the continuous-time CAPM holds, then the employee’s portfolio strategy … Melanie Cao Schulich School of Business York University 4700 KeeleSt., Toronto, Ontario, Canada M3J 1P3 Email: mcao@schulich.yorku.ca Jason Wei Rotman Faculty of Management University of Toronto 105 St. George St., Toronto, Ontario, Canada M5S 3E6 Email: wei@rotman.utoronto.ca First version: June, 2002 This version: January, 2003 Abstract Stock …

The current paper contributes to the literature by including a risky portfolio, in addition to the market portfolio and the riskfreebond, in the employee’sportfoliochoice set. This risky portfolio can be considered as a hedging index which will help reduce the non-systematic risk associated with the restricted asset. Based on the enlarged portfolio set, we analyze the employee’soptimal consumption-portfolio profile under the vesting requirement. Furthermore, we study the marginal valuation of both the restricted stock and options. The main results areas follows. First, the optimal index position is a function of the restricted stock’s weight, the residual correlation between the stock and the index, and the ratio of non systematic risks associated with the stock and the index. This optimal position cannot only reduce the impact of the illiquid stock holding on consumption, but also offset mos to ft he firm- specific risk. Therefore, it helps to improve the employee’soptimal consumption-investment policy, and better align the employee’sprivate valuation of the restricted stock with the market’s. The employee’sprivatevalueof the restricted stock is derived using the marginal rate of substitution, and is expressed as the discounted market value. This discount, termed as illiquidity discount, results from the trading restriction. As expected, this illiquidity discount is positively related to the employee’sdegreeofrisk aversion, the length of the vesting period, and the volatility of the restricted stock; it is negatively related to the partial correlation between the restricted stock and the hedging index after controlling for the market effect, which we term as”residual correlation”. With a perfect residual correlation, the impact of the trading restriction can be completely removed, and the employee’ valuation of stocks and options coincides with the market’s. Second, the employee’s private valuation of the index is higher than the market’s since the index can reduce the exposure to the non-systematic risk associated with the stock and enhance his overall utility. Effectively, the position on the index serves the purpose of partially unwinding the impact of the trading restriction. Therefore, with an optimal position on the index, the trading restriction on the company’s stock may not be as restrictive as we thought.

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