## What is the Capital Allocation Line?

Capital allocation line which also refers to the capital market line is the graph that is used to measure the risk related to securities and defines the relationship(the combination of) between risky assets and risk-free assets and it is represented by the line on the graph and it is also known as a reward to variability ratio.

It helps the investor choose the right combination of risky and risk-free assets, considering the investor’s risk appetite, and identifies the maximum return for that particular level of risk.

- Every investor wishes to earn maximum returns at minimal risk. While constructing their portfolio, every investor is faced with the issue of how much to allocate to the risky and risk-free assets.
- The aim is to optimize the return while keeping the risk at the lowest level.
- The capital allocation line helps investors determine this allocation percentage.
- It is used to identify the optimal mix of risky and risk-free returns, which results in maximum returns at minimal risk.

### Risky and Risk-Free Assets

Risk-free assets are those which do not contain any element of uncertainty as regards its return. It means that the return is guaranteed on those assets without any possibility of default. These assets generally carry a lower rate of interest, given their risk-free nature. Some example of risk-free assets are-

- T Bills;T Bills;Treasury Bills or a T-Bill controls temporary liquidity fluctuations. The Central Bank is responsible for issuing the same on behalf of the government. It is given at its redemption price and a discounted rate and is repaid when it reaches maturity.read more
- Long Term Government Bonds;
- Deposits backed by Government;
- Treasury Notes

Alternatively, risky assets are those which contain a certain level of uncertainty as regards their return. When the uncertainty, i.e., the risk is higher, the return promised on these assets is also higher. Some examples of risky assets are –

- Private Equity
- Private Debt Market Instruments;
- DerivativesDerivativesDerivatives in finance are financial instruments that derive their value from the value of the underlying asset. The underlying asset can be bonds, stocks, currency, commodities, etc. The four types of derivatives are - Option contracts, Future derivatives contracts, Swaps, Forward derivative contracts. read more
- OptionsOptionsOptions are financial contracts which allow the buyer a right, but not an obligation to execute the contract. The right is to buy or sell an asset on a specific date at a specific price which is predetermined at the contract date.read more
- Real Estate

### Components of Capital Allocation Line

The calculation of capital allocation takes into account the following components–

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For eg:

Source: Capital Allocation Line (wallstreetmojo.com)

**Risk of the Portfolio**– The risk of the portfolio would be that of the risky asset in relation to its weight in the portfolio. Risk-free assets, by definition, do not contain any risk, and therefore, the risk element would be zero.**Weights of the Assets in the Portfolio**– These are the different percentage mix in which the portfolio may be constructed using the risky and risk-free assets.**Expected Return of the Portfolio**– The expected returnExpected ReturnThe Expected Return formula is determined by applying all the Investments portfolio weights with their respective returns and doing the total of results. Expected return = (p1 * r1) + (p2 * r2) + ………… + (pn * rn), where, pi = Probability of each return and ri = Rate of return with probability. read more of the portfolio is computed, taking into account the expected return of both the risky and risk-free assets while considering the volatility (i.e., riskiness) portfolio.

### How to Calculate Capital Allocation Line?

Let us understand how the formula for the capital allocation line is determined. The return of a portfolio is calculated using the following formula –

**E**

_{p}= E(r_{s}) * w + (1-w) * E(r_{f})where,

- E
_{p }= Expected return of the portfolio - E(r
_{s}) =Expected return of the risky asset - W=Weight of the risky asset in the portfolio
- E(r
_{f}) =Expected return of the risk-free asset

Similarly, the risk of the portfolio is calculated with the following formula –

**σp =σs * ws**

Since the standard deviationStandard DeviationStandard deviation (SD) is a popular statistical tool represented by the Greek letter 'σ' to measure the variation or dispersion of a set of data values relative to its mean (average), thus interpreting the data's reliability.read more (risk quotient) of a risk-free asset is zero, to determine the risk of the portfolio, only the risky asset is considered.

Substituting the second formula in the first, we arrive at the following –

**E**

_{p }= r_{f }+ [ E(r_{s}– r_{f})/ σs**] * σp**

It is referred to as the formula for Capital Allocation Line. It can be denoted graphically as below –

The expected return is plotted along the y-axis, and the standard deviation (risk) is plotted along the x-axis. The Capital Allocation Line denotes the expected return of a portfolio at varying levels of risk. The excess return received for taking an additional risk is referred to as the risk premium – denoted in the graph.

You are free to use this image on your website, templates etc, Please provide us with an attribution linkHow to Provide Attribution?Article Link to be Hyperlinked

For eg:

Source: Capital Allocation Line (wallstreetmojo.com)

### Advantages Of Capital Allocation Line

- A portfolio allocated optimallyPortfolio Allocated OptimallyPortfolio optimization refers to the strategic process of making improvements or positive changes to the investor's portfolio containing various assets. The Sharpe ratio helps to analyze the returns from an optimal portfolio.read more based on every investor’s risk appetite and objectives.
- No reliance placed on whims or instincts. Instead, the percentages are calculated scientifically.
- It helps achieve maximum returns at minimal risk.

### Limitations

- The calculation may not be easily understandable to the normal public. It requires specialization.
- The calculation relies on various information that may not be accessible to all the investors at large.

### Conclusion

A capital allocation line is an essential tool for investors in determining their optimal portfolio mix. Although its computation mechanism is quite technical, it ensures that returns are maximum for a given level of risk.

### Recommended Articles

This article has been a guide to what is Capital Allocation Line and its definition. Here we discuss components of the capital allocation line and the formula for calculation of the capital allocation line along with advantages and limitations. You can learn more about corporate finance from the following articles –

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