# Calculation of Risk and Returns

05/02/2024Calculating risk and return is fundamental to making informed investment decisions.

**Calculation of Returns**

Returns can be calculated using different methods, depending on the type of investment and the period over which the return is measured. Here’s a basic formula for calculating the return on an investment:

Simple Return

Return = (Ending Value − Beginning Value+ Income / Beginning Value) × 100%

**Ending Value:**The value of the investment at the end of the period.**Beginning Value:**The value of the investment at the beginning of the period.**Income:**Any income generated from the investment during the period, such as dividends or interest.

Annualized Return

For investments held for multiple years, calculating an annualized return provides a compounded average return per year. The formula for annualized return is:

**n:** Number of years the investment is held.

Calculation of Risk

Risk is often quantified as the volatility of returns, measuring how much the returns on an investment fluctuate over a period. The most common measure of risk is the standard deviation of returns.

Standard Deviation

The standard deviation measures the dispersion of a dataset relative to its mean. In finance, it quantifies how much the returns of an investment deviate from the expected return.

*σ***:**Standard deviation of returns.*N***:**Total number of observations (returns).*Ri***:**Return in period*i*.**‾**Average return over*R*:*N*periods.

Beta

Beta measures the volatility or systemic risk of a security or portfolio in comparison to the market as a whole. It is used in the Capital Asset Pricing Model (CAPM) to calculate the expected return of an asset based on its beta and the expected market returns.

Beta = Covariance (Asset Returns, Market Returns) / Variance(Market Returns

- A beta of 1 indicates that the asset’s price will move with the market.

- A beta less than 1 means the asset is less volatile than the market.
- A beta greater than 1 indicates the asset is more volatile than the market.

Risk-Return Trade-off

The risk-return trade-off suggests that the potential return on any investment is correlated with the amount of risk the investor is willing to accept. Higher risk is associated with greater probability of higher return and vice versa. Investors need to balance their desire for the highest possible returns against their tolerance for risk, choosing investments that align with their risk appetite and financial goals.

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