## 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)

## 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.

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: