Risk and Return

The tradeoff between Risk and Return is the principles theme in the investment decisions. Investors take a risk when they expect to be rewarded for taking it. People invest because they hope to get a return from their investment. The Chinese symbols for risk, reproduced below, give a much better description of risk the first symbol is the symbol for “danger”, while the second is the symbol for “opportunity”, making risk a mix of danger and opportunity.

risk and return Chinese symbol

 

Return

Benefits for holding an investment over period of time are called return. Some return measures are more useful than others:

 

Components of Return

There are two components of return:

Yield: The basic component that usually comes to mind when discussing investing returns is periodic cash flows (income) on investment, either interest or dividends.

Capital Gains: The second component is also important, that is the appreciation in the price of the assets, commonly called capital gain (loss). It is simply the price change. It is the difference between the purchase price and the price at which the assets can be sold

 

Formulatotal return formula

Where:   yield component = 0 or +                                                                   Price change component = 0, +, –

 

Holding Period Return

The simplest measure of return is the holding period return. This calculation is independent of the passage of time and considers only a beginning point and an ending point. It makes no difference if the holding period return is calculated on the basis of a single share or 100 shares:

 

Formula

holding period return formula



Example # 1:

Someone might buy 100 shares of stock at Rs. 25 face value, receives a 10 cent per share dividend, and later sell the shares for Rs. 30. The holding period return is?

holding period return example

 

Example # 2:

Determine the return of the two video machines and decide which is to select?

Machine A

  • Purchase price last year: Rs. 20,000
  • Current market value: Rs. 21,500
  • After-tax cash receipt: Rs. 800

Machine B

  • Purchase price 4 years ago, but market value dropped from Rs.12,000 to Rs.11,800 this year
  • After-tax cash receipt: Rs. 3,700

 

holding period return example

Choose Machine B on the basis of high return compared to Machine A

 

Return Relative

The return relative (RR) obtains by adding 1.0 to the Holding period return.

 

Formula

return relative formula



Example # 3:

Assume that you purchase a 10 percent coupon bond @ 960, held one year and sold for 1,020. Calculate return relative?

return relative example

 

Real Rate of Return

All are the returns are nominal or money returns. They measure amount or change in the value of investment but ignore the purchasing power of the currency. To capture this dimension we have to incorporate real return of return or Inflation adjusted return. Consumer price index is used to measure the rate of inflation. To calculate inflation adjusted return we use following formula:

real rate of return formula

TRIA = Total Return Inflation Adjusted,                               NR = Nominal Return,                        IF = Rate of inflation

 

Example # 4:

Nominal return for OGDCL in 2008 was 28.57%. The rate of inflation was 1.61%. Calculate real return (inflation adjusted) for 2008?

real rate of return example

 

>> Practice Risk and Return MCQS.

 

Risk

It is not sensible to talk about investment returns without talking about risk, because investment decisions involve a trade-off between the two—return and risk are opposite sides of the same coin. Investors should be “willing to purchase a particular asset if the expected return is sufficient to compensate risk. Risk is the chance that the actual outcome of an investment will differ from the expected outcome.

 

Types of Risk

Dividing total risk into its two components, a general component and a specific component:

types of risk

 

Systematic (Market) Risk

Risk of broad macro factors affecting all securities, the investor cannot reduce or escape this part of the risk, because no matter how well he or she diversifies, the risk of the overall market cannot be avoided. Clearly, market risk is critical to all investors.

 

Nonsystematic (Non-market) Risk

Nonsystematic Risk is the variability in a security’s total returns not related to overall market variability is called the nonsystematic (non-market) risk. This risk is unique to a particular security or market so it can be reduce by diversification.

 

Measuring Future Risk (Single Investment)

Risk is often associated with the dispersion in the likely outcomes. Dispersion refers to variability. Knowing the mean of series is not enough; the investor also needs to know something about the variability in the returns.

 

Probability Distribution

A set of possible values that a random variable assumes and their associated probabilities of occurrence are called probability distribution, weather is random variable chance will be rain and no rain. Today is probability is 40% and 60 %. It is total judgmental process to access the chances or probability of occurrence an event.

probability distribution

 

Expected Rate of Return

If we multiply each possible outcome’s by its probability of occurrence and then sums these products.

 

Formula

expected rate of return formula

 

Example # 5:

Draw payoff matrix and find out expected rate of return for the following probability distribution.

expected rate of return example

 

Standard Deviation

The most commonly used measure of dispersion over some period of years is the standard deviation, which measures the deviation of each observation from the arithmetic mean of the observations and is a reliable measure of variability, because all the information in a sample is use. The standard deviation is a measure of the total risk of an asset or a portfolio. The standard deviation can be calculated by

standard deviation formula

 

Example # 6:

Calculate Standard deviation for Illustration 5 above

standard deviation example

standard deviation solved example

 

Variance

Measure of variability, the mean square deviation from mean or expected values, it is square root of standard deviation.

variance formula

 

Example # 7:

Calculate Variance for Illustration 4

variance example

 

Co-efficient of variation

The ratio of the standard deviation of a distribution to the mean of that distribution, it is a measure of relative risk.

co-efficient of variation formula

 

>>> Read Risk and Return MCQS.

 

Example # 8:

Comparison of 2 Investments in terms of Risk & Return. Which is the best Investment?

 

 

 

 

 

Name of Investment

 

 

 

 

 

Risk (Std Dev)

 

 

 

 

 

Expected Return

 

T-Bill 5% 10%

 

 

 

 

 

Shares 25% 30%

 

co-efficient of variation example

 

>>> Practice Risk and Return Quiz 1.