Finance for Business Expected Return

Question :

Determine expected return is the profit or loss that an investor anticipates from investing in an investment or assets. 

Answer :

The required rate of return project the earning capacity of a project. However, due to the economic conditions, the return rates get affected. The probability is the measures of happening or non-happening of certain events. Therefore for the calculation of the expected return, the investors are required to consider the probabilities (Martin, 2017). 

 Here, the investor is targeting investors in two different projects with different earning capacity in different probabilities. Therefore for the expected return, we are required to calculate the overall required rate of return of the assets by considering all probabilities and risk associated with it. In the given case the assets are holding an return of 10% with 30% probability, 15% return on 40% probability and 20% return on 30% probability (La Torre and Mendivil, 2018). Tus for the expected earning the for asset A thee following calculation will be required  :

Expected rate of Return Asset A:

= ( 10% * 30% ) + (15% * 40% ) + ( 20% * 30% )

=3% + 6% + 6%

=15%

The expected return of Assets A is amounting to be 15%

The expected return = (5%*40%) + (15%+20%) + (25%*40%)

= 2% + 3% + 10%

=15%

Here in the given case both projects are giving equal return thus section any of them will earn similar income.

For the standard deviation calculation the formula is sqrt of variance

Variation of Asset A = (R1-Er)^2+ (R2-Er)^2 +( R3-Er)^3

R1: Return 1 = 10%

R2: Return 2= 15%

R3: Return 3= 20%

The variance of expected retrun will be =

 (10%-15%)^2 + (15%-15%)^2 + (20%-15%)^2) / (3-1) = 0.0025

The standard deviation = sqrt of 0.0025 = 0.05= 5%

Assets B:

Variation of Asset A = (R1-Er)^2+ (R2-Er)^2 +( R3-Er)^3

R1: Return 1 = 5%

R2: Return 2= 15%

R3: Return 3= 25%

The variance of expected return will be =

 (5 %-15%)^2 + (15%-15%)^2 + (25%-15%)^2) / (3-1) = 0.010

The standard deviation = sqrt of 0.010 = 0.1 = 10%

The standard deviation of the expected return pf Asset A will be 5% and Standard Deviation of Assets B is 10%

The capital assets pricing model entails the relationship  between the expected return and systematic risk to calculate the expected return of a particular stock (AqabaBranch, 2018)

The formula for the expected return as per the CAPM is 

Risk-free rate + ( beta * ( risk premium- risk-Free rate)

The risk premium is the additional income generation capacity of a particular stock or investment that an investor will get for taking an additional risk (Sreenu, 2016). The risk premium is the market return that a particular inductor earns. Here the risk premium is amounting to be 6%.

Beta is the measure of risk factor about the chance in a company concerning the market benchmark. The beta of the stock is 1.2

Beta is the measure of stock Volatility in respect to the overall market. The beta is calculated by comparing the standard deviation of the variance of a particular stock market return with the standard deviation of the entire market return. If beta is amounting to be 1 then it showcases the changing in the companies share price will be similar to the market changes. A beta lower than one shows that the company's share will be effected lesser than the market movement or vice versa; In the given case, the beta of the selected stock is amounting to be 1.2. This shows that the share price movement of the selected company will be more than the overall market changes. Thus it is considered to be a bit risky (Yang and Hu, 2020). 

References

Eschenbach, T.G. and Lewis, N.A., 2019. Risk, standard deviation, and expected value: when should an individual start social security?. The Engineering Economist, 64(1), pp.24-39.

 La Torre, D. and Mendivil, F., 2018. Portfolio optimization under partial uncertainty and incomplete information: a probability multimeasure-based approach. Annals of Operations