# Risk and Return (Part – 2) : Measuring Expected Return of a Portfolio

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## Risk and Return of Portfolio

## Measuring Expected Return of a Portfolio

Expected return of a portfolio is the weighted average of the expected returns of the securities comprising the portfolio. Suppose a portfolio consists of total funds in each security then its expected return will be:

E (R_{P}) = w_{1}E (R_{1}) + w_{2}E (R_{2})

Where, E (R_{P}) = Expected returns on portfolio

w_{1} = Proportion of total funds invested in security 1

w** _{2}** = Proportion of total funds invested in security 2

E (R_{1}) and E (R_{2}) = Expected returns from security 1 and 2 respectively

In case there are n number of securities, the expected return on portfolio will be,

E (R_{P}) =

Where, E (R_{i}) = Expected returns from security

### Portfolio Risk

Securities in a portfolio confront two types of risk i.e.. Systematic and Unsystematic Risk.

### Systematic Risk

#### Meaning of Systematic Risk

Variation in security՚s return due to the factors related to the whole economy or market is called systematic risk. These factors include inflationary conditions in the economy, rise in interest rates, fiscal, monetary, industrial, and other policies of Government, Political instability, nuclear and natural disasters life earthquake etc. This risk affects the returns on all the securities and is perfectly related common risk. It is also referred as market or undiversified risk.

#### Components of Systematic Risk

**Market Risk**: Variability in return on most common stocks that is due to basic sweeping changes in investor expectations is referred to as market risk. Expectations of lower corporate profits, in general, may cause the larger body of common stocks to fall in price.**Interest – rate – risk**: Interest rate risk may be defined as the fluctuation in the market price of fixed income securities owing to changes in levels of the interest rate. The degree of fluctuation in the market prices of fixed income securities resulting from interest-rate-risk depends firstly on the amount of change in interest rates. The second factor affecting the degree of fluctuation in the length of the period of maturity.**Liquidity Risk**: Liquidity is the ability of a firm, company, or even an individual to pay its debts without suffering catastrophic losses. Conversely, liquidity risk stems from the lack of marketability of an investment that can՚t be bought or sold quickly enough to prevent or minimize a loss.**Default Risk**: Another risk of systematic risk is default risk. This type of risk arises because firms may eventually go bankrupt. Default risk is undiversifiable or uncontrollable as it is systematically related to the business cycle affecting all investments even though some default risk may be diversified away in a portfolio of independent investments.**Real estate risk**: The possibility of financial loss occurring as the result of owing a real estate investment. Property risk might arise from such things as liability, legal issues, partner problems that can force a sale, fire or theft, loss of rental income and purchasing property with an imperfect title.

### Unsystematic Risk

#### Meaning of Unsystematic Risk

Unsystematic risk is unique to a specific company or industry. Also known as “non-systematic risk,” “specific risk,” “diversifiable risk” or “residual risk,” in the context of an investment portfolio. Unsystematic risk can be reduced through diversification.

#### Components of Unsystematic Risk

**Business Risk**: Business risk is defined as the change that the firm will not have the ability to compete successfully with the assets that it purchases. As for example, the firm may acquire a machine that may not operate properly that may not produce salable products or that may face other operating or market difficulties that cause losses. Any operational problems are classed as a business risk.**Financial Risk**: Financial risk is associated with the way in which a company finances its investment activities. It may be defined as the change that an investment will not generate sufficient cash flows to cover interest payments on money borrowed to finance it or principal payments on the debtor to provide profits to the firm. The financial risk is an avoidable risk to the extent that managements have the freedom to decide to borrow or not to borrow funds. A firm with no debt financing has no financial risk.

## How to Calculate Portfolio Risk

Risk of a portfolio is governed by the co-variance or correlation i.e.. the relationship of change in returns of the two securities in a portfolio.

Portfolio Variance = w_{1}^{2} w_{2}^{2}_{2}^{2} + 2w_{1}w_{2}_{1}_{2}Corr (1,2)

Where, w_{1,} w_{2} are the weights of the assets in the portfolio

, _{2}^{2} is the variance of each asset

Corr (1,2) = correlation between the two assets

**The given formula indicates that**:

- By combining negatively correlated assets, the overall variability of returns i.e.. portfolio risk can be reduced.
- Smaller coefficient of correlation will tend to greater risk reduction.

## Capital Asset Pricing Model (CAPM)

- Capital Asset Pricing Model (CAPM) was developed by William Sharpe (1964) and John Linter (1965) . It has become most important model of the relationship between risk and return.
- CAPM model provides a framework to determine the expected rate of return on an asset and indicates the relationship between risk and return of the asset. It explains the mechanism to know the impact of a proposed securities investment on investor՚s overall portfolio risk and return.

**This model is based upon following important assumptions**:

**Risk and return**: CAPM assumed that only two parameters of investment in securities i.e.. , risk and expected return, form the basis of investment decisions.**Perfect capital market**: There is free flow of information to all investors at no cost. This is also meaning that investors can buy and sell securities at market price without incurring any tax or transaction cost.**Efficient portfolios**: Investors hold only efficient portfolios of securities which yields the maximum expected return for a given level of risk.**Homogeneous expectations**: Investors have homogeneous expectations regarding the risk, correlation and expected returns of securities.**Identical holding period**: Investment decisions are based on the assumptions of identical holding periods by investors.**Risk free rate**: Investors can lend or borrow the required funds at the risk-free rate of interest.

## CAPM Model

- The CAPM model shows that the expected rate of return of a security in a portfolio consists of two parts i.e.. the risk-free interest rate and risk premium. Risk – free interest rate is the reward for waiting i.e.. return with zero risk. Risk premium is the reward for undertaking systematic risk which is undiversifiable. The risk premium is equal to the difference between the expected market return and the risk – free market rate multiplied by beta factor () .
- Beta factor is the index of measurement of systematic risk. The beta of a security is the sensitivity of the security return to the overall market return. It means risk contribution of an individual security towards the total portfolio risk. If > 1 i.e.. , systematic risk of the security is more than the market risk as a whole and if < 1 i.e.. , security has less systematic risk than the market risk as a whole

**The above discussion on CAPM can be expressed in the following Equation**:

Expected Return = Risk free Return + Risk Premium

= Reward for waiting + Reward for bearing risk

Mathematically: R_{i} = R_{f} + _{m} – R_{f})

Where, R_{i} = Expected (or required) rate of return on asset i

R_{f} = Rate of return on risk – free asset

= Beta coefficient of systematic risk for asset i

_{m} Expected (or required) rate of return on the market portfolio of assets, i.e.. is average rate of return on all assets.

-Manishika