# Risk-Return Relationship

**Topics:**Random variable, Probability theory, Standard deviation

**Pages:**6 (889 words)

**Published:**July 12, 2014

estimating risk and

return on assets

1. WHAT IS RISK?

Risk is the variability of an asset’s future returns. When only one return is possible, there is no risk. When more than one return is possible, the asset is risky. The greater the variability, the greater the risk. 2. RISK – RETURN RELATIONSHIP

Investment risk is related to the probability of actually earning less than the expected return – the greater the chance of low or negative returns, the riskier the investment. Investors take on higher risk investments in expectation of earning higher returns. Of course taking risk also means that the investor does not guarantee that the investment will be recovered. 3. PROBABILITY AND PROBABILITY DISTRIBUTION

Probability – is the percentage chance that an event will occur. It range between 0 and 1.0. Probability Distribution – If all possible events or outcomes are listed and the probability is assigned to each event, the listing is called a probability distribution. It may be : An objective probability distribution is generally based on past outcomes of similar events while asubjective probability distribution is based on opinions or “educated guesses” about the likelihood that an event will have a particular future outcome. But in reality, probability distribution often combine both objective and subjective probabilities. Probability Distribution may also be:

A discrete probability distribution is an arrangement of the probabilities associated with the values of a variable that can assume a limited or finite number of values (outcomes) while a continuous probability distribution is an arrangement of probabilities associated with the values of a variable that can assume an infinite number of possible values (outcomes).

To illustrate let us answer problem No. 1

Problem 1

(a) The bar charts for Stock A and Stock B are shown in the next page. (b) Stock A’s probability distribution is skewed to the left and Stock B’s probability distribution is symmetrical. (c) Stock A’s range of returns is 24 percentage points (25 – 1) and Stock B’s range of returns is 20 points (30 – 10). (d) Stock A is riskier than Stock B because Stock A has a wider range of returns and a flatter probability distribution.

The flatter or less peaked the probability distribution of expected future returns the higher the risk of the project. A flat probability distribution has a wider range than a peaked distribution. -RANGE – is the difference between the highest and lowest possible outcome. 4. WHAT IS EXPECTED PORTFOLIO RETURNN?

The expected value of return of a single asset is the weighted average of the returns, with the weights being the probabilities of each return. Formula:

Let’s look at problem NO. 2

Problem 2

The expected value of the returns for each stock is:

Stock A

ȓA = (0.05) (0.01) + (0.20) (0.05) + (0.25) (0.10) + (0.35) (0.15) + (0.15) (0.25) = 0.1255 or 12.55%

Stock B

ȓB = (0.10) (0.10) + (0.20) (0.15) + (0.40)(0.20) + (0.20) (0.25) + (0.10) (0.30) = 0.20 or 20%

5. The risk of a single asset is measured by its standard deviation or coefficient of variation. The standard deviation measures the variability of outcomes around the expected value and is an absolute measure of risk. The coefficient of variation is the ratio of the standard deviation to the expected value and is a relative measure of risk. FORMULA OF SD and COEFFICIENT VARIATION:

Let’s look at problem No. 3

Problem 3

(a) The calculation of the expected value can be set up in tabular form.

i

pi

ri (%)

piri (%)

1

0.1

0

0

2

0.2

10

2.0

3

0.4

20

8.0

4

0.2

30

6.0

5

0.1

40

4.0

ȓ = 20.0%

(b) The calculation of the standard deviation can also be set up in tabular form. The square root of the variance, σ 2, of 120 percent is 10.95 percent (rounded).

i

ri (%)

ȓ (%)

ri (%) - ȓ (%)

(ri - ȓ) 2...

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