Risk and Return

# What is Return in Finance?

Return can be defined as the outcome of investments. It is the excess amount of cash inflows over investments. It can be defined as the difference between the investment value (cash outflow) and the sum of the cash inflows.

## Key Notes:

A return is a change in the price of an asset, investment, or project over time, which may be represented in terms of price change or percentage change.

A positive return represents a profit while a negative return marks a loss.

Returns are often annualized for comparison purposes, while a holding period return calculates the gain or loss during the entire period an investment was held.

The real return accounts for the effects of inflation and other external factors, while the nominal return is only interested in price change.

The total return for stocks includes price change as well as dividend and interest payments.

Several return ratios exist for use in fundamental analysis.

## Understanding Returns

Return represents the difference between the terminal value and the initial value of securities. Investment implies that the investor defers current consumption in order to add to his/her wealth so that he/she can consume more in the future.

So, the return on investment is concerned with the change in wealth resulting from the investment.

Such a change in wealth can either be due to cash inflows in the form of interest or dividends or caused by a change in the price of the asset.

The period during which an investor deploys funds (wealth) is termed its holding period and the return for that period is called holding period return (HR).

HPR is calculated as:

HPR = Ending value of the investment / Beginning value of the investment

An investor can convert HPR to an annual percentage rate to derive a percentage return commonly known as holding period yield (HPY).

HPY is further calculated as:

HPY = HPR-1

Again, the annual holding period return can be calculated as:

Annual HPR = (HPR) 1/N

Where N is the number of years an investment holds.

Suppose an investment is made by Tk. 200 the value of which would become art Tk.250 after 2 years.

The holding period return from the investment is:

HPR = Ending value / Beginning Value

= Tk .250 / Tk .200

= 1.25

Annual HPR = 1.25 1/N

= 11.25 1/2

= 1.1180

Therefore,

Annual HPY = Annual HPR-1

= 1.1180 -1

=0.1180

=11.80%

If the investment is held for a period of 3 years, the holding period yield then woud become:

Annual HPR = [1.25] 1/N

= 1.25 1/3

= 1.08

Therefore,

Annual HPY = Annual HPR-1

=1.08 -1

= 0.08

= 8%.

Alternatively, holding period return can be defined as the capital gains plus dividend per taka invested in the stock like:

HPR = (Capital gain+ Dividend) / Investment

HPR = [(Ending price – Beginning price) + Cash dividends] /Beginning price

The ending value of the investment can be the result of a change in the price of the investment. Annual holding period yield assumes a constant annual yield for each year.

## Patterns of Returns

Returns can be calculated in different patterns. The understanding and concepts of returns can be summarized as:

#### Total Return (TR):

Total return is the composition of current income, annual return, periodical income during period of holding of the security, and the capital gains/losses. It can be defined as the difference between initial value and the terminal value of the security.

TR can be computed as:

Total Return (TR) = Current income + Capital Gains (losses)

#### Relative Return (RR):

It is the return per unit of investment.

It is calculated by dividing the total return by the investments:

RR = TR /Investments

#### Rate of Return (R):

It is known as the percentage of return. The amount of excess money from each one hundred takas is known as the rate of return. It is expressed in terms of percentage. By percentage of returns, we know: how much an investor gets for each taka s/he invests.

#### Effective Annual Rate of return (EAR):

If the percentage of return is converted into the yearly rate of return, the result is called the effective rate of return.

It can be calculated as:

EAR = [(1 + R) 1/N ] – 1

### Historical vs. Expected Returns

Returns from security consist of income in the form of dividends or interest plus the change in capital. Total returns consist of price change and all income received during at each interval during a specific period known as duration.

Future returns are meaningful ones for decisions made today. An important use of expected return is to compare value across asset classes and across time.

Some asset allocation decisions are based on the risk premium differential, which is the difference between the expected return on assets such as stocks, bonds, or real estate and the expected return on a risk-free asset such as a Treasury bill.

An important way to assess return is to compare historical (ex-post) and expected (ex-ante) returns.

Historical returns are generated by the history of the performance of an investment over a specified time period.

Expected returns, on the other hand, are the best estimates of what returns might be over some future time period.

Historical returns are known with r certainty whereas expected returns are fraught with uncertainty i.e., they are probabilistic in nature.

The expected return would be the excess amount of money an investor expects during some holding periods in the future.

When the return is actualized after the termination of the duration, it is known as  realized return.

Realized returns can be termed as daily returns, weekly returns, monthly returns, yearly return etc. Whereas the return is estimated according to (on the basis of the present value/ market price /terminal value, the return is called estimated To return/accounting return.

## Returns of Different Securities

#### Return on Investment (ROI)

A percentage return is a return expressed as a percentage. It is known as the return on investment (ROI). ROI is the return per dollar invested. ROI is calculated by dividing the dollar return by the initial dollar investment. This ratio is multiplied by 100 to get a percentage.

#### Return on Equity (ROE)

Return on equity (ROE) is a profitability ratio calculated as net income divided by average shareholder’s equity that measures how much net income is generated per dollar of stock investment.

#### Return on Assets (ROA)

Return on assets (ROA) is a profitability ratio calculated as net income divided by average total assets that measures how much net profit is generated for each dollar invested in assets.

It determines financial leverage and whether enough is earned from asset use to cover the cost of capital. Net income divided by average total assets equals ROA.