# Return And Risk

**Return and Risk (100 points)**

Complete the following problems:

Problem #1:

You are the investment consultant for a Saudi Arabian hospital to assess the risk for its future investments.

There are three potential opportunities:

- Investing in Clinic A, or Clinic B, or Clinic C.
- They have the following probabilities about their return on investment:

**What is the expected return for each clinic?**

The expected return is calculated by multiplying the probability of Return by Return (r), in this case, the expected return for each clinic is determined by multiplying the possibility of recovery by the respective Return for each clinic, this is done in excel, and the results are as follows:

Years |
Probability of Return |
Return for Clinic A |
Return for Clinic B |
Return for Clinic C |
E. R for Clinic A |
E.R for Clinic B |
E. R for Clinic C |

1 | 0.10 | 5% | 1% | -10% | 0.005 | 0.001 | -0.01 |

2 | 0.20 | 6% | 3% | 0% | 0.012 | 0.006 | 0 |

3 | 0.40 | 7% | 4% | 5% | 0.028 | 0.016 | 0.02 |

4 | 0.20 | 8% | 5% | 15% | 0.016 | 0.01 | 0.03 |

5 | 0.10 | 9% | 10% | 20% | 0.009 | 0.01 | 0.02 |

Expected Return on Respective Clinics | 0.07 | 0.043 | 0.06 |

These results mean that the investor expects to get 0.07 percent returns if he invests in Clinic A, 0.043% returns in Clinic B, and 0.06% returns in clinic C.

**Calculate the standard deviation of return for each clinic?**

The standard deviation measures the extent of variability of possible returns from the expected return. Standard deviation is the square root of the variance (Heiny, 2018).

From the calculation, the standard deviation of return for Clinic A is 0.010954451. The standard deviation of return for Clinic B is 0.02193712, while the standard deviation of return for Clinic C is 0.083066239. It is clear that Clinic A has a lower standard deviation of return than clinics B and C. Therefore, the typical standard deviation indicates that the prices are calm; hence, the investments come with low risk.

**If the hospital is risk-averse, which clinic would you recommend?**

To determine the recommended Clinic; it is essential to compare the Clinics

Comparison of the Clinics

Clinic |
Expected Return |
Standard Deviation |

A | 0.07 | 0.010954451 |

B | 0.043 | 0.021931712 |

C | 0.06 | 0.083066239 |

Being risk-averse means that the hospital is trying to evade or prevent risk; therefore, it should consider investing in a clinic with low risk. From the Table, Clinic A has the lowest standard deviation than Clinics B and C. The lower the standard deviation, the less risky the Clinic is as far as investment is considered. I would therefore recommend Clinic A because the typical standard deviation indicates that the investment prices are calm; hence the assets come with low risk. (Dionne, 2013).

**If the hospital wants the highest, return which clinic would you recommend?**

To determine the recommended Clinic; it is essential to compare the Clinics

Comparison of the Clinics

Clinic |
Expected Return |
Standard Deviation |

A | 0.07 | 0.010954451 |

B | 0.043 | 0.021931712 |

C | 0.06 | 0.083066239 |

From the Table, Clinic A has the highest Expected Return (0.07%) than Clinics B (0.043%) and C (0.06%). The higher the expected return, the more returns a Clinic has. If the hospital wants the most elevated, return they should invest in Clinic A (Wang, 2017).

**If the hospital wants a good return but with a medium level of risk, which clinic would you recommend?**

If the hospital wants a good return but with a medium level of risk, then I would recommend Clinic B

Clinic |
Expected Return |
Standard Deviation |

A | 0.07 | 0.010954451 |

B | 0.043 | 0.021931712 |

C | 0.06 | 0.083066239 |

Problem #2:

The hospital invests in several Mutual Funds

Calculate the required rate of return for each fund.

Mutual Fund |
Beta |
Required Rate of Return |

A | 0.75 | 0.105 |

B | 0.55 | 0.093 |

C | 1.25 | 0.135 |

Risk-free rate | 0.06 | |

Market Rate | 0.12 |

The required rate of return (RRR) refers to the minimum amount of profit (return) that the investor anticipates receiving/ get for investing in a particular investment. RRR helps to determine the nature of the profitability of the project. Therefore, the required rate of return for each fund is indicated in the above table. Fund C has more return (0.135) than Funds A and B. However, Fund B has the lowest return (0.093).

Problem #3:

Mutual Fund D is made up of the following stocks

Based on this data, calculate the portfolio’s return and Beta.

The portfolio return is the gain or loss realized by the investment portfolio having various investment types. Portfolios usually focus on delivering returns depending on the stated objectives of the given investment plan and the risk tolerance of the given investors targeted by the portfolio. The portfolio return is calculated using the following formulas:

Portfolio’s Return= Weighted Beta * Expected Return

Weighted Beta = Beta *the percent of an overall portfolio (Vollmer, 2015).

Stock |
% of Portfolio |
Beta |
Expected Return |
Weighted Beta |
Portfolio’s Return |

1 | 25% | 0.75 | 0.17 | 0.1875 | 0.031875 |

2 | 35% | 1 | 0.18 | 0.35 | 0.063 |

3 | 10% | 0.9 | 0.22 | 0.09 | 0.0198 |

4 | 17% | 1.45 | 0.16 | 0.2465 | 0.03944 |

5 | 13% | 1.25 | 0.19 | 0.1625 | 0.030875 |

100% | |||||

Portfolio’s Return= | 0.18499 |

Therefore, the portfolio’s return = 0.18499 while Beta for each stock is as shown in the above table. The Portfolio Beta can be obtained by summing up the Beta for all stock which would give us a beta of 1.0365 (Frömmel, 2013).

Problem #4:

You are provided with the following information about a portfolio

Calculate the required rate of return for the portfolio using CAPM

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To Calculate the required rate of return for the portfolio using CAPM, the following procedures are followed:

- We Subtract the risk-free rate of recovery from the market Risk premium.
- We then Multiply the above result by the beta.
- And then, Add the result in step two to the risk-free rate; this will give us the required rate of return.

Applying the above procedure gives the following result:

Column1 |
Column2 |

Risk-free-rate | 0.05 |

Market Risk Premium | 0.12 |

Beta | 1.55 |

The required rate of return for the portfolio | 0.1585 |

Therefore, the required rate of return for the portfolio is 0.158

**References**

Dionne, G. (2013). Risk management: History, definition, and critique. *Risk Management and Insurance Review*, *16*(2), 147-166. https://doi.org/10.1111/rmir.12016

Frömmel, M. (2013). *Portfolios and investments* (3rd ed.). BoD – Books on Demand.

Heiny, K. (2018). *Standard deviation*. Fourth Estate.

Vollmer, M. (2015). A beta-return efficient portfolio optimization following the CAPM. https://doi.org/10.1007/978-3-658-06634-5

Wang, P. (2017). Future realized return, firm-specific risk, and the implied expected return. *Abacus*, *54*(1), 105-132. https://doi.org/10.1111/abac.12109

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