According to Portfolio Theory, by diversifying, investors can eliminate unsystematic risk (also known as diversifiable risk or specific risk) related to individual stocks, but not systematic risk (market risk, or the general perils of investing). The Capital Asset Pricing Model (CAPM) describes the relationship between systematic risk and expected return for assets/stocks.
Capital Market Equilibrium
In the context of capital markets, equilibrium occurs when all securities are priced such that the quantity supplied equals the quantity demanded. At this point, all investors have adjusted their portfolios to their desired risk levels, and there is no incentive to trade further as all available information is already reflected in security prices.
- Demand and Supply Balancing: Equilibrium is achieved when the expected returns on securities are in balance with their risk, taking into account the risk-free rate and market return.
- No Arbitrage: In equilibrium, there are no arbitrage opportunities — no way to make a risk-free profit by buying and selling securities.
CAPM operates under the assumption of market equilibrium. It assumes that all investors are rational, risk-averse, and aim to maximize their expected utility, leading to a market where prices reflect all available information (efficient market hypothesis). In a state of capital market equilibrium, the only risk that investors are compensated for is systematic risk, as unsystematic (or specific) risk can be diversified away in a well-constructed portfolio. In a state of equilibrium, asset prices are such that the expected returns, as calculated by CAPM, are aligned with the inherent risks of those assets.
CAPM (Capital Asset Pricing Model)
CAPM is a model that establishes a relationship between risk and expected return. It's used to estimate an asset’s expected return given its systematic risk (also known as market risk or non-diversifiable risk). It is primarily used for pricing risky securities like stocks.
CAPM Formula
- Risk-Free Rate (R_f): The return on an investment with no risk, typically represented by government bonds.
- Beta: A measure of how much risk the investment will add to a portfolio that already includes the market portfolio. It shows the sensitivity of the asset’s returns to market returns.
- If a stock is riskier than the market, it will have a beta greater than one. (The stock is more volatile than the market) If a stock has a beta of less than one, the formula assumes it will reduce the risk of a portfolio.
- Beta is typically calculated using regression analysis on historical data, showing how the return of the stock is related to the return of the market.
- Market Risk Premium: The additional return expected by investors for taking on the additional risk of investing in the market as opposed to risk-free securities.
- Note: Determining the exact value for the market return rate can be challenging, as it involves forecasting future market performance. Investors use many different approaches.
Investors anticipate rewards for both the inherent risk of an investment and the monetary value over time. In the CAPM formula, the risk-free rate reflects the monetary value over time. The formula's remaining elements compensate for the extra risk assumed by the investor.
The purpose of the CAPM formula is to assess if a stock is valued appropriately considering its risk and the time value of money in relation to its anticipated return. Essentially, by understanding the distinct components of the CAPM, one can determine if a stock's current market price aligns with its expected return.
Assumptions of CAPM
- Market Efficiency: Markets are assumed to be efficient, meaning all information is already reflected in security prices.
- Single-Period Model: CAPM is a single-period model, typically considering a time frame like one year.
- Risk Preferences: All investors are rational and averse to risk, and they look to maximize their utility.
- Homogeneous Expectations: All investors have the same expectations for an asset's returns.
- Borrowing and Lending: Investors can borrow and lend unlimited amounts at the risk-free rate.
- No Transaction Costs or Taxes: There are no costs associated with buying or selling securities, and no taxes are considered in the model.
CAPM Example Scenario
Suppose an investor is considering purchasing a stock that is currently priced at $150 per share and offers a 4% annual dividend. Let's assume this stock has a beta of 1.5 relative to the market, indicating that it is more volatile than a broad market index like the S&P 500. Additionally, assume that the risk-free rate is 2% and the investor expects the market to increase in value by 7% annually.
Using the CAPM formula, we can calculate the expected return of the stock:
- Expected Return = 2% + 1.5*(7%-2%) = 9.5%
Valuation
- Stock Price: $150 per share
- Annual Dividend: 4% (which equals $6 per share, as 4% of $150)
- Expected Return (CAPM): 9.5%
Total Present value is sum of Present Value of Dividends and present value of the expected future sale price:
- If the dividends are expected to stay constant, Present Value of Dividend is: $6/0.095 = $63.16
- Let's say you expect to sell the stock after 5 years for $180. Then, Present Value of this expected future pricing is: $180/((1.095)^5) = $114.34
Thus, Total Present Value is $63.16+$114.34 = $177.5, which means that the current stock price of $150 is undervalued.
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