Question

display relation between risk and standard deviation and give three example by refering measure of risk please use it : www.zenwealth.com/businessfinanceonline/RR/MeasuresOfRisk.html

Answer 1

In many sectors of the finance industry, risk measurement is a primary focus. While it can play a role in economics and accounting, the impact of accurate or faulty risk measurement is most clearly illustrated in the investment sector. Whether investing in stocks, options or mutual funds, knowing the probability that a security moves in an unexpected way can be the difference between a well-placed trade and bankruptcy.

standard deviation measures the average amount by which individual data points differ from the mean

Relation Between risk and Standard deviation

Standard deviation is used as an indicator of market volatility and therefore of risk. The more unpredictable the price action and the wider the range, the greater the risk. When using standard deviation to measure risk in the stock market, the underlying assumption is that the majority of price activity follows the pattern of a normal distribution.The more volatile a security, the larger the standard deviation. The standard deviation is calculated as the positive square root of the variance

The formula for Variance is

where:

• N = the number of states,
• p_i = the probability of state i,
• R_i = the return on the stock in state i, and
• E[R] = the expected return on the stock.

Standard deviation is positive Square root of variance.

Examples of measured Risk

Security A

State	Probability	Return (Ri)
1	20%	5%	.005625	0.001125
2	30%	10%	.000625	0.0001875
3	30%	15%	.000625	0.0001875
4	20%	20%	.005625	0.001125
	Variance			0.002625

Expected Return = .20(5%) + .30(10%) + .30(15%) + .20(20%) = 12.5%

Standard deviation = =.0512 = 5.12%

Measure risk of security A is 5.12%

Security B

State	Probability	Return (Ri)
1	20%	50%	0.09	0.018
2	30%	30%	0.01	0.003
3	30%	10%	0.01	0.003
4	20%	-10%	0.09	0.018
	Variance			0.042

Expected Return = .20(50%) + .30(30%) + .30(10%) + .20(-10%) = 20 %

Standard deviation = =.2049 = 20.49%

Measure risk of security B is 20.49%

Security C

State	Probability	Return (Ri)
1	20%	45%	0.1089	0.02178
2	30%	15%	0.009	0.0027
3	30%	5%	0.0049	0.00147
4	20%	-15%	0.0729	0.01458
	Variance			0.04053

Expected Return = .20(45%) + .30(15%) + .30(5%) + .20(-15%) = 12%

Standard deviation = =.2013 = 20.13%

Measure risk of security C is 20.13%

With the same probability Security A has lowest risk which is clear from its positive return consolidated near average line where as Security B & C has Scattered returns thus risk is high in them resulting into high standard deviation.