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## Questions:

This assessment requires qualitative explanations that display your understanding of the concepts of risk and return. The article of Simon Hoyle gives some understanding of the concepts of risk and return. However, it was published in a newspaper where the target readers were not all educated in finance.

You are required to answer the following questions while providing deeper insights about the concepts of risk and return than those that are provided in the article.

Read the article by Simon Hoyle and answer questions

### Q1.

Explain how the risk of shares can be calculated by the standard deviation. Your explanation should include the usage of the dispersion statistics, the normal distribution, and the probability, and how those concepts are utilized in real life finance.

### Q2.

Apparently, Simon Hoyle’s article did not mention what would happen to the risk if an investor decided to buy more than one share. Explain how adding new shares to a portfolio can affect the risk and return of that portfolio. You should use the concepts of correlation coefficient and the standard deviation in your explanations.

Use the concepts of correlation coefficient and the standard deviation in your explanations.

## Answers:

### 1. Risk Calculation Using Standard Deviation

**Example:**

Values: 4, 6, 8, 12, 20, 30, 24, 28, 40, 48

Mean = Sum of Values/Total No. of Values

= (4+6+8+12+20+30+24+28+40+44) / 10 = 22

(Value-Mean)^{2} = [(4-22)^{2}=324, (6-22)^{2}=256, (8-22)^{2}=196, (12-22)^{2}=100, (20-22)^{2}=4, (30-22)^{2}=64, (24-22)^{2}=4, (28-22)^{2}=36, (40-22)^{2}=324, (48-22)^{2}=676]

Mean of Squared Values = (324+256+196+100+4+64+4+36+324+676) / 10 = 198.4

Standard deviation = [{Sum of (Value-Mean)^{2}} / Total No. of Values]^{1/2}

= (198.4)^{1/2} = 14.08545

Risk measurement is the core concern for a smart investor, for which standard deviation is most commonly used measurement metrics. Standard deviation is best measure for calculating dispersion, widely used in studying variability of returns of an investment from a particular strategy (Damodaran, 2016). It is often interpreted as a measure of the degree of uncertainty, and thus risk, associated with a particular security or investment portfolio.

The base assumption while using standard deviation to measure risk in the stock is a normal distribution. Here 68% times value fall within a single standard deviation of the mean; 95% time’s values are within two standard deviations of mean and 99.7% times within 3 standard deviations of the mean (Vernimmen, 2014). Like here if the stock price is $100 and SD is $14.08, 65% chance that price is in range of $114 to $86; 95% certain for the price to range between $128 to $72; and 99.7% certainty to range between $142 to $ 58.

Probability distribution makes use of finding the possibility of getting the desired stock price in order to assess the return as calculated in association with the risk factor making use of standard deviation as a tool.

### 2. Risk And Return In Case Of Portfolio Investment

The smart investor believes in saying “don’t keep all eggs in one basket”, which here means investment in diversified stocks to mitigate the risk that arises from single stock investment by the distribution of risk among various types of stock (Brealey, 2012). That means if one stock is not performing well, that is compensated by other averagely or high performing stocks of the portfolio. The Expected Return of a Portfolio can be computed arriving at the weighted average of the expected returns on various stocks in a portfolio.

**Example:**

Stock | Weight | Return |

A | 50% | 20% |

B | 30% | 15% |

C | 20% | 30% |

Return of Portfolio = E[R_{p}] = E[R_{A}]*W_{1} + E[R_{B}]*W_{2} + E[R_{C}]*W_{3}_{}

= 0.50(20%) + 0.30(15%) + 0.20(30%)

= 20.5%

The correlation coefficient measures the degree of association of two variables, ranging from -1.0 to 1.0. The negative relationship shows the variables move in opposite directions whereas positive relation shows stocks move in a similar direction. Diversification benefits can be gained by adding low or negatively correlated stocks (Ehrhardt, 2016). On the other hand, standard deviations measure dispersion from its average. The correlation coefficient is derived by dividing covariance by the product of the two standard deviations, to arrive at a normalized account of the statistic.

## References

Brealey, Richard A., Stewart C. Myers, Franklin Allen, and Pitabas Mohanty. Principles of corporate finance. Tata McGraw-Hill Education, 2012.

Damodaran, Aswath. Damodaran on valuation: security analysis for investment and corporate finance. Vol. 324. John Wiley & Sons, 2016.

Ehrhardt, Michael C., and Eugene F. Brigham. Corporate finance: A focused approach. Cengage Learning, 2016.

Vernimmen, Pierre, Pascal Quiry, Maurizio Dallocchio, Yann Le Fur, and Antonio Salvi. Corporate finance: theory and practice. John Wiley & Sons, 2014.

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