Expected Return Calculator

Understanding Expected Return

Expected Return $E(R)$ is a foundational concept in investment analysis, corporate finance, and modern portfolio theory. It estimates the anticipated profit or loss an investor can expect on an investment relative to its initial cost, based on historical rates of return or probability distributions across various market conditions.

Probability-Weighted Scenario Formula

When evaluating economic scenarios (such as Bull, Normal, or Bear market states), expected return is calculated as the sum of each scenario return weighted by its probability:

$$E(R) = \sum_{i=1}^{n} P_i \times R_i$$

Where $P_i$ represents the probability of scenario $i$ and $R_i$ is the return in that scenario.

The CAPM Model Formula

The Capital Asset Pricing Model (CAPM) calculates expected return based on systemic market risk ($\beta$):

$$E(R) = R_f + \beta \times (R_m - R_f)$$

Where:

• $R_f$: Risk-Free Rate (e.g. US Treasury yield)
• $\beta$: Beta parameter measuring sensitivity to overall market volatility
• $R_m$: Expected return of the overall market index
• $(R_m - R_f)$: Market risk premium

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