**Portfolio of Investment**

The mean historical rate of return (HPY) for a portfolio of investments is measured as the weighted average of the HPYs for the individual investments in the portfolio, or the overall percent change in value of the original portfolio.

The weights used in computing the averages are the relative beginning market values for each investment; this is referred to as dollar-weighted or value-weighted mean rate of return.

Consider the following example:

Investment | No. of shares | Beginning price | Beginning market value | Ending price | Ending market value |

A | 100,000 | $10 | $1,000,000 | $12 | $1,200,000 |

B | 200,000 | 20 | 4,000,000 | 21 | 4,200,000 |

C | 500,000 | 30 | 15,000,000 | 33 | 16,500,000 |

Total | $20,000,000 | $21,900,000 |

Here,

HPR =21,900,000/20,000,000

=1.095

HPY =1.095 − 1

=0.095

=9:5%

**Calculating Expected Rates of Return**

Expected Return = Summation of (Probability of Return) × (Possible Return)

Consider the following example.

Economic Conditions | Probability | Rate of Return |

Strong economy, no inflation | 0.15 | 0.20 |

Weak economy, above-average inflation | 0.15 | -0.20 |

No major change in economy | 0.70 | 0.10 |

**Calculating Expected Rates of Return**

The computation of the expected rate of return is as follows:

[(0.15) x (0:20) + (0:15)(− 0:20) + (0:70)(0.10)

= 0.07

=7%

**Measuring the Risk of Expected Rates of Return**

Risk in investment is associated with return. The risk of an investment cannot be measured without reference to return. The investors try to measure or quantify the risk associated with investment before making final decision about the investment. This can be done by

(i) the variance calculation, and

(ii) the standard deviation of the estimated distribution of expected returns.

**Standard Deviation**

The standard deviation is the square root of the variance:

SD = σ2

**Explanation of the results of SD:**

Larger the value of SD for an expected rate of return, the greater the uncertainty, or risk, of the investment.

**Relative Measure of Risk**

In some cases, an un adjusted variance or standard deviation can be misleading. If conditions for two or more investment alternatives are not similar—that is, if there are major differences in the expected rates of return—it is necessary to use a measure of relative variability to indicate risk per unit of expected return.The relative variability of risk can be measured by the coefficient of variation (CV).

**DETERMINANTS OF REQUIRED RATES OF RETURN**

There are three elements of required rate of return which are further influenced by a number of other factors.

(1) The time value of money during the period of investment,

(2) The expected rate of inflation during the period, and

(3) Risk involved.

**Factors Influencing the Determinants of Required Rate of Return**

The factors influence the determinants of required rate of return:

(1) The Real Risk-Free Rate

(2) The Nominal Risk-Free Rate (NRFR)

(3) Risk Premium

**The Real Risk-Free Rate**

The real risk-free rate (RRFR) is the basic interest rate, assuming no inflation and no uncertainty about future flows.

An investor in an inflation-free economy who knew with certainty what cash flows he or she would receive at what time would demand the RRFR on an investment.

**The Nominal Risk-Free Rate (NRFR)**

The real interest rate after taking inflation and changes of monetary policy into account is called nominal rate.

It is influenced by the condition of the capital market and the rise of prices in an economy.

**Risk Premium**

The extra amount of return required by the investor beyond the risk free interest rate is called risk premium.

Various types of risks can result in the uncertainty of the investment such as the political instability of the country and other risks connected with the situation of the country.

**Types of Risks**

**(1) Systemic Risk:** The risk which cannot be diversified and belong to the nature of the business sector is called systemic risk.

**(2) Unsystematic Risk :**The risk which can be diversified and is related to the industry is called unsystematic risk.

**Major Sources of Uncertainty & Risk**

The sources of fundamental risk are:

- Business risk
- Financial risk
- Liquidity risk
- Exchange rate risk
- Country risk