# Conduct a one-way sensitivity analysis by varying the probability of being sunny. Use base-value +/-25% with 11 steps. [Hint: your original file has to set up the probability of rain as a formula of (1 – the probability of being sunny), rather than a value of 0.25.] Report a sensitivity graph and a strategy region graph (EMV and variations in the probability) and discuss which strategy is the best in terms of EMV

A bank manager considers an investment strategy. She has three options: a stock for a big company, a bond and a stock for a start-up company, whose stock returns are denoted by SB, BB, and SS, respectively. It is known that SB and BB follow normal distributions: SB~N(8%,10%) and BB~N(2%,1%) and SB and BB have a correlation of -0.5. SS are independent of both SB and BB, and has discrete distribution:

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- Using @Risk or equivalent software, simulate returns of SB, BB and SS and fill out the following summary statistics of simulated data. Use percentage returns up to 2 decimal points (for instance, 3.99%).

BB | SB | SS | |

Mean | |||

Median | |||

Standard deviations | |||

Interquartile Range |

- The bank manager asks you which investment you recommend among the following four strategies.

- For each investment strategy, report a histogram of simulated returns and also report a table including summary measures (Minimum, Maximum, Mean, 90% CI, Mode, Median, Std Dev).

- Among four strategies, which one is the best and the worst strategy in terms of average return?

- Which one is the safest strategy in terms of standard deviations?

- Under some bank regulation, the bank manager maintains the Value-at-Risk 5% of the portfolio return being -2.5% or above. Find a portfolio that satisfies the regulation and achieve an average return of 4% or above. Report your portfolio and simulation outcomes (histogram, mean and 5% percentile).

**Questions 2 (40 marks=5 + 5 + 10 + 10 + 10)**

Suppose that you were wondering whether to open a café. There are two choices: Strategy #1 is not to open (Not IN) and Strategy #2 is to open (IN). The table below shows unit price and cost per customer and a fixed cost per day in dollars (note: you have to pay the fixed cost, such as a rent every day regardless of the number of customers.)

Strategy | #1 | #2 |

Decision | Not IN | IN |

Unit Price | 0 | 3.5 |

Unit Cost | 0 | 1.5 |

Fixed Cost | 0 | 500 |

The number of customers varies according to weather condition and you consider the following probability table.

Probability | #Customer | |

Sunny | 0.75 | 600 |

Rainy | 0.25 | 260 |

If you do not open a café, then you can invest your asset into a fixed income security, which generates a return of $380 per day.

- Fill out a table below regarding risk profiles for profits according to strategies and weather conditions. [Hint: profit is given by # customers * (unit price – unit cost) – fixed cost.]

Strategy | #1 | #2 | Probability |

Sunny | |||

Rainy |

- Obtain Expected Monetary Value (EMV) for two strategies.

Strategy | #1 | #2 |

EMV |

- Draw a decision tree by using PrecisionTree software. [Hint: your tree has four end nodes.]

- Conduct a one-way sensitivity analysis by varying the probability of being sunny. Use base-value +/-25% with 11 steps. [Hint: your original file has to set up the probability of rain as a formula of (1 – the probability of being sunny), rather than a value of 0.25.] Report a sensitivity graph and a strategy region graph (EMV and variations in the probability) and discuss which strategy is the best in terms of EMV (30 words or less).

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