Tips for Investment Banking/S&T Technical Questions - CAPM & Black Scholes Model
This question's a staple in an #investmentbankinginterview especially if you’re aspiring to crack a #salesandtrading grad job or internship.
💡 Black Scholes Model: This foundation model determines the theoretical value of derivatives other investment instruments, taking into account the impact of time and other risk factors. The formula helps to value an option based on the underlying security’s price, its dividend yield, the option’s time to expiration, the strike price, the risk-free rate, the implied volatility, and a cumulative density function.
No transaction costs are involved in buying the option, market movements are random, the risk-free rate and volatility of the underlying asset are known and remain constant, and returns on the underlying asset are log-normally distributed. (Originally the formula assumed no dividend payouts would happen during the life of the option but this flaw was corrected later)
💡 BSM’s Limitations:
It doesn’t address how U.S. options can be exercised before the expiration date (so it's applicable to European options only). The model assumes that it’s possible to hedge delta without transaction costs or even liquidity constraints. It assumes dividends, volatility, and risk-free rates to remain constant over the option's life and do not account for taxes, commissions, trading costs, or taxes which can skew valuations from real-world scenarios. Also, knowing the level of volatility and assuming it remains constant is erroneous. The model is inefficient in calculating implied volatility and assumes that returns follow a random walk.
💡 Capital Asset Pricing Model:
It's used to determine the expected return on an investment and appropriate discount rate for a company’s cash flows. As an analyst, you’ll need CAPM to determine the fair price of an investment like a stock. If Stock X is riskier than Stock Y, the price of the riskier Stock X should be lower to compensate investors for the higher risk.
Once you calculate the risky stock's rate of return using CAPM, that rate can then be used to discount the investment's future cash flows to their present value and assess the asset’s fair value. You can then compare it to its market price and if your price estimate is lower, the stock is considered to be overvalued.
Formula: ra = rrf + Ba (rm-rrf)
rrf = the rate of return for a risk-free security
rm = the broad market's expected rate of return
Ba = beta of the asset
💡 CAPM’s drawbacks:
Using beta to measure risk can be unreliable. The beta of a company is estimated via a regression model that correlates the past performance of a company relative to the market which is an inaccurate indicator of future share price performance. The capital structure (debt/equity ratio) of companies also progressively changes over time, which can alter their risk profiles and performance.
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