Stock Options Encourage Managers to Maximize Shareholder Value - Essay Example

of the of the Finance Project Introduction Stock options are a form of compensation granted to an employee, by an employer, in lieu of salary and wages. Stock options grant employees the right to purchase a certain number of shares at a given price. Traditionally, firms have compensated their employees through some combination of salaries, commissions, or bonuses. Less prevalent was compensation tied to firm's performance, such as stock and/or stock options. Historically, performance-based compensation was designed for corporate executives and officers of the firm. This form of compensation helped align the interests of management and shareholders. Stock options encourage managers to maximize shareholder value. Although stock options were once reserved for upper management, there has been a trend to include more employees. Generally, the future purchase price, or strike price, is equal to the market price of the stock at the time of grant. When an employee exercises options, he or she pays the firm the strike price for the shares, regardless of the then- current market price. Employees usually remain with the firm for a specified period before options vest. Upon vesting, the employees may exercise their options. If an employee leaves the firm, outstanding vested and unvested options are forfeited or cancelled. Options not exercised by a date specified in the option contract will expire. When an employee decides to exercise their stock options, they may either purchase the underlying stock at a discounted price or receive an equivalent cash premium. This transfer from the firm to the employee becomes part of the employee's taxable income for the year. Firms now grant stock options to a much broader range of employees for many reasons. A firm's motivation in implementing a stock option plan includes increased employee productivity, the attraction and retention of valuable human capital, reduction of short-run compensation costs, increased cash flows, and higher levels of book income. Individuals, employers, and the government are all affected by the widespread use of stock option compensation. However another aspect that is affected by stock options is economic forecasters. Income from stock options is more volatile than traditional forms of compensation, such as wages and salaries. Stock options' ultimate value to the employee depends on the future stock performance. Consequently, the stock option value is uncertain at the time of grant. Literature Review Arbitrage pricing arguments can be extended to allow for diversifiable risks. In equilibrium, these risks will be fully diversifiable and have zero prices. Thus every asset can be priced exactly (or approximately) as a linear combination of a relatively small number of common factors. Although this is instructive for introducing basic ideas of arbitrage, aggregation, and diversification, we require a multiperiod framework to capture a range of intertemporal problems. For example, we would like to investigate the term structure of interest rates, complicated multiperiod derivative securities, the dynamics of stock prices, and dynamic hedging strategies. It will turn out that our two-period analysis has laid an important foundation for this analysis. By choosing an appropriate dynamic framework, we can generalize our two-date results, and obtain obvious sophisticated reinterpretations of familiar results. Pastor and Stambaugh (2000) provide further details through an investigation of the portfolio choices of an investor seeking a mean-variance efficient portfolio by comparing the risk based model of Fama, and French (1993) and the characteristic based model of Daniel, K. & Titman, (1-33). They report that there is virtually no difference between the risk- and characteristic-based models, as both lead to similar portfolio choices within the investment universe. (Michael, et.al. 119) While debate continues over explanatory basis of the various multifactor models, the essence of the argument remains the same--multiple factors are required to capture the cross-section of stock returns. Miller (95-101) corroborates this view, arguing that although the single-beta CAPM managed to withstand more than three decades of intense scrutiny, the current consensus is that a single risk factor is not sufficient for describing the cross-section of expected stock returns. Malkiel (1999) also observes that there is still much debate within the academic community on risk measurement and much more empirical testing needs to be done. This is a view shared by Campbell, Lo and Mackinlay (1997) who forward that the usefulness of multifactor models will not be fully known until sufficient new data become available to provide an out-of-sample check on their performance. However, it is worth noting that the bulk of the existing research in the area of empirical asset pricing relates to the United States and other developed capital markets. (Michael, et.al. 119) Finance Theory Evolution In particular, dynamic asset-pricing models based on diffusion processes can be viewed as a special case of a more general dynamic factor model. Furthermore, by taking an appropriate basis, simple discrete models can mimic their more complex continuous-time counterparts. This discrete model provides an accessible and highly flexible framework for integrating asset-pricing theory. In addition the model can be adapted to incorporate fiat money and nominal asset returns, multiple currencies and exchange rates, transaction costs, taxes, and many other features. These variations have been developed recently, or are in the process of development. This unification of finance theory has found a parallel in modern macroeconomics, where representative agent economies have been analyzed to investigate real and pricing variables. The development of finance theory has been rapid. Not only has it provided highly flexible models, but they have found wide application in financial markets. These developments have been important in providing a coherent framework for thinking about existing financial markets and decision-making; and for creating ways of thinking about new financial products. It is ironic that abstract ideas developed in the 1950s and 1960s, which once were thought to have limited application, should become the common language of financial markets. An arbitrageur is one who tries to make a profit from minor inconsistencies between exchange rates in different foreign exchange markets. They are not risk takers. Speculators and arbitrageurs are key to the success of a multinational corporation. They enable treasuries to be able to know the future transaction rates and help them pass the risk onto someone else. Treasuries risk management has objectives such as, to minimize costs, maximize revenue and to stabilize margins in the future. Treasuries make use of "hedging products" provided by speculators and arbitrageurs. Examples of these products are forward contracts or option contracts. They help to reduce the volatility of a firm's profits and cash generation, and will help to reduce the volatility of the value of the firm. There are several arguments against the use of speculators and arbitrageurs, the first being purchasing power parity. According to this theory, movements in exchange rate offset price level changes. If purchasing power parity were to hold immutably and with no time lags, there would be no such thing as exposure to exchange risk and consequently no need to hedge. However this theory has problems. In the real world the adjustment between changes in price levels and exchange rates is anything but immediate. There are long time lags. Also, with respect to the price level indices of two countries; if the increase in the price levels of carrots in the US and potatoes in Ireland do not correspond to the increases in the inflation levels of their respective countries, there will be a relative price risk. Capital Asset Pricing According to Capital Asset Pricing model, the essential aspect of risk that matters is systematic risk. If forward exchange and interest hedge contracts are priced according to the capital asset pricing model, all that the firm does by entering into these kinds of contract is to move along the security market line. If this is so then there is no addition to the firm. Another argument begins against the use of speculators and arbitrageurs and ends up pointing in the opposite direction. This is the self-insurance and market efficiency argument. Currency and interest rate markets do not provide bargains only fair gamble based on fair prices. Gains and losses will tend to average out over the long run. Hence an open position is essentially the same as a hedged position. Considering the treasurer is not necessarily seeking excess returns but merely trying to establish a risk/return profile, with which the management feels comfortable, why he would want to expose himself to variable currency and interest rates. The main argument for the use of speculators and arbitrageurs by a treasury is that hedging reduces the probability of financial distress. By reducing cash flow volatility, hedging reduces the probability of the firm getting into financial difficulty and bearing the consequent cost of such distress. By hedging the firm reduces the probability that its cash throw-off will be insufficient to enable it to pursue its planned strategy. Companies that provide service agreements make a long-term commitment to their customers. The value customers place on these agreements depends on their perception of the financial viability of the firm. If the future of the firm is in doubt, customers will place less value on the service back up and may turn to a competitor or demand lower price to compensate. By this, there is an evident impact upon profit and cash generation of the firm. With the probability of financial distress increased by an absence of hedging suppliers of debt capital might demand higher returns to compensate for higher expected bankruptcy costs. Given Data Set We have data on two companies - General Motors (GM) and General Mills (GIS). Also we have data on the S&P500 index which represents the "market portfolio." Values are observing on monthly set of data over a period of 5 years. Using Single Index Model (Questions 1- 4) 1. Compute the returns per month using the equation Result of returns per month for General Motors (GM), General Mills (GIS) and S&P500 are given in excel sheet by using this form of formula: x 100 2. Use these returns to use the single index model, i.e., Ordinary Least Squares Regression Model for GIS Coefficients Standard Error t Stat P-value Intercept 1.791473 0.528604 3.389064 0.001278 R_GIS 0.173214 0.086584 2.000528 0.050215 So = 1.7914 and = 0.1732 Therefore Rt = 1.7914 + (0.1732RM) Ordinary Least Squares Regression Model for GM Coefficients Standard Error t Stat P-value Intercept 1.436493 0.458966 3.12985 0.002757 R_GM 0.295145 0.058761 5.022774 5.34E-06 So = 1.436 and = 0.295 Therefore Rt = 1.436 + (0.295RM) 3. Show the proportion of total risk (variance) that can be eliminated through diversification. That is, show the proportions of systematic and unsystematic risk. Proportion of Total Risk (Variance) There is no perfect response to the inquiry of the riskiness. Sometimes the possible results vary extensively, and the strategy being pursued must also be considered. Sale of a put or call exposes the researcher to tremendous losses, whereas purchase of the call or put has penetratingly limited loss possibilities. Enclosed alternatives present limited risk, and protective puts or portfolio hedging are destined to reduce risk. Presently there is no uncertainty, though, that some options trades can nearby significant risk. One cause for the attractiveness of options as investment is that they offer influence. For the total amount of the premium, the consumer "controls" 100 shares of stock, so that a $ 1 change in the value of the stock fundamental and in-the-money option results in a much larger modify in the premium. 4. Compute the covariance and correlation matrices for the three assets (two stocks plus the S&P500 index). Select the two assets that have the lowest correlation and form an equally weighted portfolio from those two assets. Repeat steps 2-4. Show that, and Covariance R_GIS R_GM S&P500 R_GIS 35.35298 R_GM 1.199619 56.94317 S&P500 6.12363 16.80651 16.16766 Correlation R_GIS R_GM S&P500 R_GIS 1 R_GM 0.026737 1 S&P500 0.256137 0.553902 1 Two lowest correlation can be observed by R_GM vs. R_GIS = 0.026737 and S&P500 vs. R_GIS = 0.256137 eighted Portfolio between GIS and GM w_GIS w_GM Var Stdev R_P 1 0 35.35298 5.945837 1.385346 0.9 0.1 29.42128 5.424138 1.448387 0.8 0.2 25.28751 5.028669 1.511428 0.7 0.3 22.95169 4.790792 1.574469 0.6 0.4 22.4138 4.734321 1.63751 0.5 0.5 23.67385 4.865578 1.700551 0.4 0.6 26.73184 5.170284 1.763592 0.3 0.7 31.58776 5.620299 1.826633 0.2 0.8 38.24163 6.183982 1.889674 0.1 0.9 46.69343 6.833259 1.952715 0 1 56.94317 7.54607 2.015756 5. Using reward to risk ratios, determine if an arbitrage opportunity exists, and how to obtain the return if there is one. Arbitrage (GIS) w_GIS 2.640209 3.657604 W_F -1.64021 -0.68342 R_P 2.974184 R_SP500 2.031435 Arb. 0.942749 Black Scholes Option Pricing Model (Questions 6-8) 6. Compute the annual variance of returns using continuous returns. Continuous returns are computed using the equation Then, compute the annual variance as The variance of is multiplied by 12 because the data is monthly. Also, use just one year's worth of data in computing. Dec 98 -99 31.62 GIS 47.34 GM 34.86 0.09755 59.38 0.226602 33.49 -0.04009 54.92 -0.07808 31.38 -0.06508 57.87 0.052322 31.05 -0.01057 59.24 0.023398 34.13 0.094578 55.82 -0.05946 34.13 0 53.39 -0.04451 35.90 0.050561 49.45 -0.07666 36.30 0.01108 54.02 0.088392 35.16 -0.03191 51.32 -0.05127 38.57 0.092566 57.44 0.11266 33.35 -0.14542 60.62 0.053884 31.63 -0.05295 59.71 -0.01513 0.257182 0.320057 7. Compute the value of a call and put option on General Motors with an exercise price of $55, and General Mills with an exercise price of $30. The time to expiration for all options is 3 months. Use the Black-Scholes option pricing model to compute this value and state its assumptions. The current value of the stock is the last traded price. Lastly, break the call and put option prices into intrinsic value and speculative premium components. Computations are given below: GIS GM S 31.63 59.71 X 55 30 rf 0.05 0.05 T 0.25 0.25 0.257182 0.320057 2 0.066143 0.066143 d_1 -4.14071 4.459253 d_2 -4.26931 4.299225 N(d_1) 1.73E-05 0.999996 N(d_2) 9.8E-06 0.999991 Black-Scholes model works well if the stock price is stable. But the model is less accurate when it comes to pricing the options in volatile markets such as the ones in which high technology companies participate. Those opposed to expensing options at the grant date feel that options are not a company expense, but rather costs shifted to shareholders. Footnoting the expense should permit analysts to properly price the stock without distorting a firm's profit and loss statement. Since there are many estimates used in stock data, recording a major calculations using a very complex and potentially inaccurate pricing model would further complicate financial statements. 8. Discuss the relationship between S, X, r, T and 2 and call and put option prices. Black-Scholes Option Pricing Model Call option value is based on the original B-S model and has been expressed as a function of five parameters: CB-S = f(S, 2, X, T, rf) Where S is the price of underlying asset (or can say stock for this particular case) 2 is the instantaneous variance of the asset returns X is the price of exercise T is the expiration time in months (=T/12) and rf is the risk-free rate Through web definitions we define call option - it gives the holder the right to buy the underlying asset by a certain data for a certain price. And a put option gives the holder the right to sell the underlying asset by a certain date for a certain price. These assumptions have been utilized in developing valuation models for alternatives: 1. The rate of return on the stock follows a lognormal distribution. This means that the logarithm of 1 plus the rate of return follows the normal, or bell-shaped, curve. (The assumption ensures continuous trading - the stock rate of return distribution is continuous.) 2. The risk-free rate and variance of the return on the stock are constant throughout the option's life. (The two variables are nonstochastic.) 3. There are no taxes or transaction costs. 4. The stock pays no dividends. 5. The calls are European, which does not allow for early exercise. 9. Discuss how call and put options can be used to hedge a short or long position in the share. Black-Scholes Output Model for GIS Stocks GIS IV TP Call 1.5028E-05 0 1.5E-05 Put 22.6867941 23.37 -0.68321 Black-Scholes Output Model for GM Stocks GM IV TP Call 30.0826743 29.71 0.372674 Put 8.3564E-06 0 8.36E-06 Works Cited Black F. and M Scholes, "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, 1973, 637-654. Black, F. "Noise," Journal of Finance, vol. 41, pp. 529-543 (1986). Black, F., and M Scholes, "The pricing of options and corporate liabilities," Journal of Political Economy, 1973, 637-654. Bodie, Zvi, Alex Kane, and Alan J. Marcus. Investments. 4th ed. Boston: Irwin/McGraw-Hill, 1999. Campbell, J.Y., Lo, A.W. & MacKinlay, A.C. 1997, The Econometrics of Financial Markets, Princeton University Press, New Jersey. Chance, Don M. An Introduction to Derivatives. 4th ed. Fort Worth, TX: Dryden Press, 1998. Daniel, K. & Titman, S. 1997, "Evidence on the characteristics of cross sectional variation in stock returns', Journal of Finance, vol. 52, pp. 1-33. Fama, E.F. & French, K.R. 1993, 'Common risk factors in the returns on stocks and bonds', Journal of Financial Economics, vol. 33, pp. 3-56. Kolb, Robert W. Futures, Options, and Swaps. 3rd ed. Malden, MA: Blackwell Publishers, 1999. Malkiel, B.G. 1999, A Random Walk Down Wall Street, W.W. Norton and Company, New York. Merton H. Miller. "The Derivatives Revolution After Thirty Years," Journal of Portfolio Management (May 1999). Merton H. Miller. "The History of Finance." Journal of Portfolio Management 25, 4 (Summer 1999). 95-101 Michael E. Drew, Tony Naughton , Madhu Veeraraghavan. Firm Size, Book-to-Market Equity and Security Returns: Evidence from the Shanghai Stock Exchange. Australian Journal of Management. Volume: 28. Issue: 2. 2003. Australian Graduate School Of Management. P. 119 Reilly, Frank K., and Keith C. Brown. Investment Analysis and Portfolio Management. 5th ed. Fort Worth, TX: Dryden Press, 1997, 237-295. Sharpe, W. F., "Capital Asset Prices: A theory of market equilibrium under conditions of risk," Journal of Finance, 1964, 425-442. Read More