This CAPM Calculator accurately computes the theoretical expected return for an asset based on systematic risk. It is a fundamental tool for portfolio management and capital budgeting decisions.
Welcome to the **CAPM Calculator** (Capital Asset Pricing Model). CAPM is a foundational model in finance used to determine the theoretically appropriate required rate of return for an asset, given its risk. The model links four core variables—Risk-Free Rate ($R_f$), Expected Market Return ($R_m$), Beta ($\beta$), and Expected Return ($R_e$). Input any three of these values to solve for the missing fourth variable.
CAPM Calculator
CAPM Formula
The core CAPM equation is:
$$ R_e = R_f + \beta \times (R_m – R_f) $$
Where $R_m – R_f$ is the Market Risk Premium.
1. Solve for Expected Return ($R_e$):
$$ R_e = R_f + \beta \times (R_m – R_f) $$
2. Solve for Beta ($\beta$):
$$ \beta = \frac{R_e – R_f}{R_m – R_f} $$
3. Solve for Risk-Free Rate ($R_f$):
$$ R_f = \frac{R_e – \beta \times R_m}{1 – \beta} $$
4. Solve for Market Return ($R_m$):
$$ R_m = R_f + \frac{R_e – R_f}{\beta} $$
Formula Source: Investopedia – CAPM
Variables Explained
- Rf – Risk-Free Rate: The theoretical rate of return on an investment with zero risk, usually represented by the yield on short-term government securities (e.g., 10-year Treasury note).
- Rm – Expected Market Return: The expected return of the overall market or a broad index (e.g., S&P 500).
- β – Beta: A measure of the asset’s systematic risk (volatility) relative to the overall market. A beta of 1 means the asset moves with the market.
- Re – Expected Return: The required rate of return for the asset based on the risk taken.
Related Calculators
What is CAPM?
The Capital Asset Pricing Model (CAPM) describes the relationship between systematic risk and expected return for assets, particularly stocks. It is widely used throughout finance for pricing risky securities and generating expected returns for assets given the risk of those assets and the cost of capital. The model is based on the premise that investors must be compensated for taking risk (measured by Beta) and for the time value of money (measured by the Risk-Free Rate, $R_f$).
The difference between the expected market return ($R_m$) and the risk-free rate ($R_f$) is known as the **Market Risk Premium**. This premium is the additional return investors expect for taking on the average risk of the market. CAPM states that the only risk an investor should be compensated for is systematic risk (market risk), which cannot be diversified away.
The result of the CAPM formula, $R_e$, is the minimum return an investor should require from an investment to justify holding it. If the expected return of an asset is higher than the calculated $R_e$, it may be considered undervalued.
How to Calculate Expected Return (Example)
Assume a **Risk-Free Rate ($R_f$)** of **3.0%**, an **Expected Market Return ($R_m$)** of **9.0%**, and a stock **Beta ($\beta$)** of **1.5**.
- Determine Market Risk Premium ($R_m – R_f$): $9.0\% – 3.0\% = 6.0\%$ (or $0.06$).
- Calculate Risk Premium for the Stock: $\beta \times (R_m – R_f) = 1.5 \times 6.0\% = 9.0\%$ (or $0.09$).
- Apply CAPM Formula: $R_e = R_f + \text{Stock Risk Premium} = 3.0\% + 9.0\%$.
- Determine Expected Return: $R_e = 12.0\%$. The required return for this stock is **12.00%**.
Frequently Asked Questions (FAQ)
A Beta of 1.0 means the asset’s price moves in perfect tandem with the overall market. If the market increases by 5%, the asset is also expected to increase by 5%.
What is the primary assumption of CAPM?The primary assumption is that all investors are rational, risk-averse, and seek to maximize return for a given level of risk. It also assumes all investors have homogeneous expectations and access to the same information.
How is the Risk-Free Rate determined in practice?The Risk-Free Rate ($R_f$) is typically proxied by the yield on a long-term government bond (e.g., 10-year US Treasury bond) in the local currency, as government debt is generally considered to carry the lowest possible risk of default.
Can Beta be negative?Yes, Beta can be negative. A negative Beta means the asset’s price tends to move in the opposite direction of the market. While rare, assets like gold or certain derivatives sometimes exhibit negative Beta.