## What is Investment Analysis?

Investment analysis involves assessing and evaluating the potentiality of investment based on risk and return.

## Measures of Return and Risk

This lesson will provide insight into how to measure the rate of return and the risk involved in an investment accurately. Basically, we examine ways to quantify return and risk. The lesson will consider how to measure both.

(1) historical rates of return and risk and

(2) expected rates of return and risk.

## Measures of Historical Rates of Return

To measure historical rates of return, we have to know the first Holding Period (HP) and Holding Period Return (HPR).

The period during which you own investment is called its holding period, and the return for that period is the holding period return (HPR).

For example, if you commit \$200 to an investment at the beginning of the year and you get back \$220 at the end of the year, what are the HP and HPR? Here, HP is 1 year, and ## Interpretation of HPR

A value greater than 1.0 reflects an increase in your wealth, which means that you received a positive rate of return during the period.

A value less than 1.0 means that you suffered a decline in wealth, which indicates that you had a negative return during the period.

An HPR of zero indicates that you lost all your money (wealth) invested in this asset.

## HPR in Percentage terms on an annual basis

The conversion of HPR to annual percentage rates makes it easier to directly compare alternative investments that have markedly different characteristics.

To do this, the holding period yield (HPY) is to be calculated as follows.

HPY = HPR − 1

In our example, HPY = 1:10 − 1

= 0:10 = 10%

## HPR in Percentage terms on an annual basis

If there is more than one-year investment holding period (HP), Annual HPR is calculated by:

Annual HPR = (HPR)1/n

where n = number of years the investment is held.

For example, an investment that costs \$250 and is worth \$350 after being held for two years. What are annual HPR and HPY?

## HPR in Percentage terms on an annual basis

The HPR  is as follows: You may experience a decline in your wealth value. For example, beginning value is \$500 and the ending value of the investment is \$400, then the computation is as follows:

## HPR in Percentage terms on an annual basis

If there is a multiple-year loss over two years, for example, the ending value of the investment is \$750 and the beginning value is \$ 1,000, the value would be computed as follows.

## Computing Mean Historical Returns

Over a number of years, a single investment will likely give high rates of return during some years and low rates of return, or possibly negative rates of return, during others. Your analysis should consider each of these returns, but you also want a summary figure that indicates this investment’s typical experience, or the rate of return you might expect to receive if you owned this investment over an extended period of time. You can derive such a summary figure by computing the mean annual rate of return (its HPY) for this investment over some period of time.

Alternatively, you might want to evaluate a portfolio of investments that might include similar investments (for example, all stocks or all bonds) or a combination of investments (for example, stocks, bonds, and real estate). In this instance, you would calculate the mean rate of return for this portfolio of investments for an individual year or for a number of years.

Single Investment:

Given a set of annual rates of return (HPYs) for an individual investment, there are two summary measures of return performance.

(1) arithmetic mean return,

(2) the second is the geometric mean return

## Arithmetic & Geometric Mean Return where, ΣHPY = the sum of annual holding period yields

GM = [πHPR]1/n − 1

where, π = the product of the annual holding period returns as follows:

• (HPR1) × (HPR2) . . . (HPRn)

## Arithmetic vs Geometric

Consider an investment with the following data: ## AM vs GM. Which one is best?

Investors are typically concerned with long-term performance when comparing alternative investments. GM is considered a superior measure of the long-term mean rate of return because it indicates the compound annual rate of return based on the ending value of the investment versus its beginning value.

AM is best used as an expected value for an individual year, while the GM is the best measure of long-term performance since it measures the compound annual rate of return for the asset being measured.

When rates of return are the same for all years, the GM will be equal to the AM. If the rates of return vary over the years, the GM will always be lower than the AM.

Consider, for example, a security that increases in price from \$50 to \$100 during year 1 and drops back to \$50 during year 2. The annual HPYs would be: This would give an AM rate of return of  25%

This investment brought no change in wealth and therefore no return, yet the AM rate of return is computed to be 25%. The GM rate of return would be 0.

This answer of a 0 percent rate of return accurately measures the fact that there was no change in wealth from this investment over the two-year period.

## 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 the 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: 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. 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 the return. The risk of an investment cannot be measured without reference to return. The investors try to measure or quantify the risk associated with the investment before making the 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.

## Variance Analysis of Investment

The variance for the potential investment is calculated as follows:

Variance (σ2) = Interpretation of variance result:

Larger the variance for an expected rate of return, the greater the dispersion of expected returns and the greater the uncertainty, or risk, of the investment.

Variance Analysis of Investment

In perfect certainty, there is no variance of return because there is no deviation from expectations and, therefore, no risk or uncertainty.

For example, if there is no risk in investment, the variance result would be 0.

## Standard Deviation

The standard deviation is the square root of the variance: 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 unadjusted 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).

The coefficient of variation can be calculated as follows: This measure of relative variability and risk is used by financial analysts to compare alternative investments with widely different rates of return and standard deviations of returns.

## Relative Measure of Risk

Consider the following two investments: Comparing absolute measures of risk, investment B appears to be riskier because it has a standard deviation of 7 percent versus 5 percent for investment A.

In contrast, the CV figures show that investment B has less relative variability or lower risk per unit of expected return because it has a substantially higher expected rate of return as follows.

Coefficient of variance (CV) of Investment A = 0.05/0.07 = 0.714

Coefficient of variance (CV) of Investment B = 0.07/0.012 = 0.583

## DETERMINANTS OF REQUIRED RATES OF RETURN

There are three elements of the 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 the 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 the 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 the 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: