# Question: 1 assume that you manage a risky portfolio with the...

###### Question details

1. assume that you manage a risky portfolio with the expected rate of return are of 0.15 and a variance after.09. The T bill week is still .06. Your client chooses to invest 0.60 of the portfolios in your portfolio at the balance in T-bills

a. You What is the expected return and standard deviation of your client’s portfolio

b. Suppose your portfolio includes the following in the given proportions:

share X -20%,

share Y -40%

and the balance in share Z

What are the investment proportions of each stock in your client’s overall portfolio including the position of the T bills?

c. What is the sharpe ratio (S) of your risky portfolio and your client’s overall portfolio? Interpret the sharpe ratio

Question 2

XYZ stock price and dividend history are the following

Year |
Share price at the beginning of the year |
Dividend paid at the end of the year |

2014 |
70 |
3 |

2015 |
68 |
4 |

2016 |
70 |
2 |

2017 |
65 |
2 |

2018 |
67 |
5 |

And investor buy three shares of XYZ at the beginning Off 2007, Buy another two shares At the beginning of 2008, sells one share at the beginning of the 2009 and sells all four remaining shares at beginning of 2018

Using the above information calculate:

a. Arithmetic and geometric average time weighted rates of return for the investor

b. What is the dollar weighed rate of return?

Question 3

Scenario |
Probability |
HPR % |

Recession |
.10 |
-6 |

Normal growth |
.70 |
25 |

Boom |
0.20 |
35 |

Using the above table calculate

a. Expected return

b. Standard deviation

Question 4

Company |
Expected return % |
Variance % |

X |
12 |
1 |

Y |
14 |
3 |

The correlation between share X and Y is negative 30%

Using the above table calculate

a. Weights for the minimum variance portfolio

b. Expected return of the minimum variance portfolio

c. Standard deviation of the minimum variance portfolio

Question 5

Suppose rf= 6.75% and a well-diversified portfolio P has a beta of 1.4 and an alpha pf 1% when regressed against a systematic factor S. Another well diversified portfolio Q has a beta of 1 and alpha of 1.65%

A. Using the other information, explain if there is any arbitrage opportunity

B. If there is an arbitrage opportunity, what action would you take to capitalise on this opportunity?