# What is the relationship between CAPM and the Cost of Equity?

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Sharpe’s Model of Capital Asset Pricing Model results in the cost of equity estimation. Sharpe’s model calculates the cost of capital by building a relationship between risk and return. As per the model, a risk-free return is expected out of every investment. The expectation is greater than that is based on the given amount of risk associated with the chosen investment. The model states that the anticipated or required rate of return is equal to the sum of the risk-free rate and a certain premium dependent on the systematic risk associated with the security.

## Systematic Risk and Unsystematic Risk

Systematic Risk is unavoidable. This risk contains factors that affect the overall market and not a single or a few stocks in the market viz. macroeconomic conditions, inflation all over the world, etc. Beta (β) represents the systematic risk in finance and statistics.

Unsystematic Risk is the stock- or industry-specific risk that does not affect the whole market. Unsystematic risks can be diversified and reduced to a great extent.

## Capital Asset Pricing Model (CAPM)

The result of Sharpe’s model is a simple formula based on the explanation just given above.

$$\mathrm{k_{e}=R_{f}+(R_{m}-R_{f})\beta}$$

where,

$$\mathrm{k_{e}= Required \:rate \:of \:return\: or\: cost \:of\: equity}$$

$$\mathrm{R_{f}= Risk-free \:rate \:of \:return,\: normally\: the \:treasury \:interest\: rate \:offered\: by\: the \:government.}$$

$$\mathrm{R_{m}= It \:is\: the \:expected \:return \:from\: the\: Market \:Portfolio.}$$

$$\mathrm{{\beta}= Beta \:is \:a \:measure \:of\: risk \:in \:the \:equation.}$$

Market Portfolio is the conceptual portfolio of shares that contains all the shares trading in the market multiplied with their weights as their market capitalization. Practically, one can take a portfolio that represents all the industries and has a sufficient amount of stock of each industry to sufficiently diversify the stock-specific risks.

The objective of a market portfolio is the need for a portfolio that has diversified all the avoidable risks, and which cannot be more than the total market portfolio.

Beta measures the responsiveness of an individual stock’s shifts due to changes in market return. The higher the beta of security, the bigger would be the required rate of return by the investor.

Beta impacts the required return as it has a direct multiplication impact on the premium. When the beta is 1, the stock return is equal to the market return. If beta is less than 1, a stock return would be less than the market return; and if it is greater than 1, the required return of the stock will be greater than the market return.