Abstract
Options can be generalized as contracts that can be bought at a given price enabling one to buy or sell an asset or security at a possible future profit. If the profitable opportunity does not arise, the price paid for the option is foregone. An understanding of the theory and analysis of options is useful to the financial managers in enabling them to estimate trends and may be employed to temporarily secure assets until a decision is made whether to buy or not and to hold on to new projects or innovations until a final decision.
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Notes
- 1.
Straddles, straps, and strips, combinations of calls and puts, might pose problems for the Malkiel-Quandt notation. For example, if one purchases one call and one put at the same exercise price on the identical stock, it would appear that the investor will never lose.
$$ {\displaystyle \begin{array}{l}\begin{array}{c}\mathrm{straddle}\\ {}\mathrm{buyer}\end{array}=\begin{array}{c}\mathrm{call}\\ {}\mathrm{buyer}\end{array}+\begin{array}{c}\mathrm{put}\\ {}\mathrm{buyer}\end{array}\\ {}\ \left[\begin{array}{c}+1\\ {}\kern1.12em 0\end{array}\right]\kern1em +\kern1em \left[\begin{array}{c}\kern1em 0\\ {}+1\end{array}\right]\kern1em =\kern1em \left[\begin{array}{c}+1\\ {}+1\end{array}\right]\end{array}} $$One could purchase a 80 September call on IBM for $5.10 and an 80 IBM September put for $0.35. If the investor buys a straddle, one invests $5.45 (or $545 in the 100 share position) in the position. The investor purchases volatility in buying a straddle on profits only if the price rises above $59.38 or falls below $50.63. A straddle buyer does not care which event (advance or decline) occurs as long as the volatility is very large. A strike might lead one to buy a straddle on the firm’s stock; one could profit on the put if the strike is long and violent and the call if the strike is settled quickly and cheaply. The Malkiel-Quandt positions do not offer the investor an insight into the volatility problems in purchasing a straddle. A straddle writer appears to consistently lose in the Malkiel-Quandt analysis:
$$ \left[\begin{array}{c}-1\\ {}\kern1.12em 0\end{array}\right]\kern1em +\kern1em \left[\begin{array}{c}\kern1em 0\\ {}-1\end{array}\right]\kern1em =\kern1em \left[\begin{array}{c}-1\\ {}-1\end{array}\right] $$However, in reality, the writer wins as long as the price fluctuates between $50.63 and $59.38. The straddle writer wins as long as the stock volatility is low. Anything that reduces the stock volatility enhances the profitability of the straddle writer; for example, a merger, particularly a conglomerate merger, reduces systematic risk and total risk. A merger announcement could lend one to write straddles on the acquiring firm’s stock.
A strap is when one has two calls and one put in an option portfolio. A strap buyer is not completely certain about the course of a stock’s movement; however, the u = buyer is leaning toward an upward stock movement. One can easily see this in the Malkiel-Quandt notation:
$$ {\displaystyle \begin{array}{c}\mathrm{strip}\ \\ {}\mathrm{buyer}\end{array}}\kern1.5em 2\kern0.5em \left[\begin{array}{c}+1\\ {}\kern1em 0\end{array}\right]\kern1em +\kern1em \left[\begin{array}{c}\kern1em 0\\ {}+1\end{array}\right]\kern1em =\kern1em \left[\begin{array}{c}+2\\ {}+1\end{array}\right] $$One must be aware of the numerous (3) transaction costs and premiums associated with straps. In our Alcoa example, the 55 October strap would cost $737.50 [2($3) + $1.375 = $7.375]. Therefore, the break-even price range is $47.63 and $58.69 [$55 + $7.28/2]. One profits at a 2:1 ratio as the stock price advances above $55. A strip is two puts and one call. A strip purchaser is somewhat confused but more pessimistic than optimistic about the stock price movement. The Malkiel-Quandt notation for a strip purchaser is
$$ {\displaystyle \begin{array}{c}\mathrm{strip}\kern1.75em \\ {}\mathrm{purchaser}\end{array}}\kern2em \left[\begin{array}{c}+1\\ {}\kern1em 0\end{array}\right]+2\left[\begin{array}{c}\kern1em 0\\ {}+1\end{array}\right]=\left[\begin{array}{c}+1\\ {}+2\end{array}\right] $$Straddles, straps, and strips offer investors and portfolio managers opportunities to alter portfolio return distributions.
- 2.
Wall Street quickly adopted the Black and Scholes OPM to the extent that even practitioners into their 50s and 60s who cannot take a derivative, total or partial, have hired “computer jocks” to program the OPM into their computers or use their H-P calculators.
- 3.
The authors believe few stockholders view the call option feature as truly meaningful. If the market value of the firm falls below the value of debt, the stockholders’ value is zero.
- 4.
The stockholders own the firm and agree to pay the bondholders the value of the firm until the value of the assets exceeds the face value of the debt. If the value of assets is less than the face value of debt, then the equity holders must declare bankruptcy, and the bondholders can take possession of the firm. When a firm uses leverage, then the risk of the firm increases and the return on equity rises (linearly). The beta of the firm rises with leverage as a linear function:
$$ {\beta}_{jL}={\beta}_{ju}\left[1+\frac{D}{E}\left(1-t\right)\right] $$where
-
βjL = firm j beta with leverage
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βju = firm j beta with leverage
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D = debt
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E = equity
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T = corporate tax rate
The cost of equity is a linear function of the firm beta as the reader saw in chapter “Risk and Return of Equity and the Capital Asset Pricing Model” with the Capital Asset Pricing Model (CAPM):
$$ \mathrm{Ke}={\mathrm{R}}_{\mathrm{F}}+\left[\mathrm{E}\left({\mathrm{R}}_{\mathrm{M}}\right)\hbox{--} {\mathrm{R}}_{\mathrm{F}}\right]\upbeta $$The beta in the CAPM is a levered beta for the vast majority of firms in our economy. The concept of options and leverage is important because equity is like a call option on the firm. Equity holders can undertake risky projects that may increase the volatility of the firm. The value of the call is a function of volatility, and higher risk increases the value of equity at the expense of debt.
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Guerard, J.B., Saxena, A., Gultekin, M. (2021). Options. In: Quantitative Corporate Finance. Springer, Cham. https://doi.org/10.1007/978-3-030-43547-9_16
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