In a recent one day workshop on Introductory Derivatives for equity analysts we were asked what is the difference between the way equities are analyzed and the options are analyzed. A one sentence answer was: equity analysis focuses on expected return of a stock, using linear deterministic models of dividends, earnings, etc. whereas options analysis is concerned only with analyzing the volatility of a stock, using stochastic models of random price movements.

**Point 1: Volatility versus the Direction of the Stock Price **

Consider the problem: there are two non-dividend paying stocks in the same industry, A and B and both of them have the same value today, say $100. Over the last twelve months stock A is falling by 5% every month and stock B is increasing by 5% every month. This is an idealized and theoretical example but will serve to illustrate an important point. Both stocks will have the same percentage historical volatility (in fact, the percentage volatility of the stocks will be zero, thereby making the asset degenerate, which is an interesting mathematical case but doesn't happen in real life). Also, consider one year at them money call options on both the stocks, with the risk free rate being the same for both.

In the absence of any other information about the stocks or the economy if you ask an equity investor which stock will he buy then he will instinctively reply stock B, which is increasing by 5% every month. If you ask an options trader which call option will he buy, the call on stock A or the call on stock B, then he will answer: "it doesn't matter". Both the call options will have same value and therefore the options trader will be indifferent between the call on A or the call on B.

Thus, while the equity investor will buy the stock B, given its direction, the options trader will remain indifferent between the calls on either stock. And this highlights the great divide between the way equities are analyzed and options on equities (or any derivative security) are analyzed.

Option prices, at the point of analysis, depend on the initial value of the stock at that point in time and the volatility of the stock (of course, other parameters such as interest rate, time to maturity, etc. remaining constant). It is the volatility of a stock that completely and singularly determines the price of an option. Nothing else matters. Most importantly, the return of a stock does not matter at all. So as long as the volatility of the two stocks are the same, then given the same initial value of each stock the value of the option turns out to be same. The fact that one stock is falling and the other is rising has done nothing to alter the volatility of the stocks. On the other hand, equity prices are dependent on the return of a stock. The return enters the equation via the linear Capital Asset Pricing Model, and through various linear parameterization and forecast of quantities like dividends, earnings, etc. The entire framework of analysis for equities is linear in return and the expectation of the return in future. Thus a higher expected return for stock B will prompt the equity investor to buy stock B.

**Point 2: Randomness versus Fundamental Analysis **

Options and other derivatives are analyzed using Quantitative Analysis. The basic framework of quantitative analysis is to treat stocks, interest rates, FX, etc. as random variables - or what we call "stochastic" - and the only shock that causes randomness in these assets is the volatility. In other words, all information, knowledge and risk are subsumed in volatility of an asset (stocks, interest rates, etc.) and this shock causes the asset price to move in any direction, canceling out any expected return. All that matters for options analysis is to understand, analyze and model this shock, this randomness, i.e. the volatility of the stock or the asset. Modelling randomness or volatility is the key to modelling options and derivatives.

Equities, on the other hand, are analyzed using Fundamental Analysis and Capital Asset Pricing Model. In fundamental analysis there is no place for randomness. It is a deterministic and linear framework which analyzes the balance sheet and financial statements of a company to derive a linear expected return projection. Dividends, expected earnings, cash flow, etc. all these quantities are projected linearly to be aligned with the expectation of a stock appreciating or depreciating in a linear fashion. In capital asset pricing model as well the volatility of a stock is relevant but only so far as it relates to the volatility of the overall market and overriding criterion of estimating stock price is the expected market return.

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