Investment Assignment 1
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Q1 An investor bought a stock and held it for a month. The stock did not pay any dividends during that period. The investor estimated the realized monthly net return, which was 9.05%. If the investor sold the stock at the end of the month for $150.29, what was the purchasing price of the share? Round your answer to two decimals.
To calculate the purchasing price of the share, you can use the formula for calculating the realized monthly net return:
Realized Monthly Net Return = [(Selling Price - Purchasing Price) / Purchasing Price] * 100
Given:
- Realized Monthly Net Return = 9.05% (0.0905)
- Selling Price = $150.29
Let "Purchasing Price" be denoted as P. We can rearrange the formula to solve for P:
0.0905 = [($150.29 - P) / P] * 100
Now, let's solve for P:
0.0905 = [($150.29 - P) / P] * 100
0.0905 = [(150.29 - P) / P] * 100
0.0905 = (150.29 - P) / P
Now, we can isolate P:
P * 0.0905 = 150.29 - P
0.0905P + P = 150.29
1.0905P = 150.29
P = 150.29 / 1.0905
P ≈ 137.59
So, the purchasing price of the share was approximately $137.59 when rounded to two decimals.
Q2 An investor assumes that there are only two possible states of the world for next year, "boom" or "recession", both with equal probability of occurring. If the "recession" scenario occurs, a stock will pay an annual dividend of $0.29, and the stock price will be $11.1 by the end of the year.
If the "boom" scenario occurs, a stock will pay an annual dividend of $0.52, and the stock price will be $18.68 by the end of the year. If the stock price today is $11.04, what is the annual expected net return estimated using this assumptions? Round your intermediate steps (if necessary) and your answer to four decimals. Do not use percentage format! That is, 1.234% should be input as 0.0123
To calculate the annual expected net return based on the given assumptions, we can use the
concept of expected value. The expected annual net return can be calculated as the weighted average of the returns in each scenario, with each scenario weighted by its probability of occurring.
Given:
- Two possible states of the world: "boom" and "recession," each with equal probability.
- In the "recession" scenario, the stock pays a dividend of $0.29, and the end-of-year stock price is $11.1.
- In the "boom" scenario, the stock pays a dividend of $0.52, and the end-of-year stock price is $18.68.
- The current stock price today is $11.04.
Let's calculate the expected annual net return:
1. Calculate the expected dividend (D) and expected end-of-year stock price (P) based on the
two scenarios:
- "Recession" scenario (R):
- Dividend (DR) = $0.29
- End-of-year stock price (PR) = $11.1
- "Boom" scenario (B):
- Dividend (DB) = $0.52
- End-of-year stock price (PB) = $18.68
2. Calculate the expected return (ER) for each scenario, which is the total return including dividends and capital gains, by considering the change in stock price:
- Expected return in the "Recession" scenario (ER_R):
- ER_R = (DR + (PR - P)) / P
- ER_R = ($0.29 + ($11.1 - $11.04)) / $11.04
- ER_R ≈ 0.0054 (rounded to four decimal places)
- Expected return in the "Boom" scenario (ER_B):
- ER_B = (DB + (PB - P)) / P
- ER_B = ($0.52 + ($18.68 - $11.04)) / $11.04
- ER_B ≈ 0.3721 (rounded to four decimal places)
3. Calculate the weighted average of the expected returns using the equal probabilities of the two scenarios:
- Expected Annual Net Return (EANR):
- EANR = (ER_R + ER_B) / 2
- EANR = (0.0054 + 0.3721) / 2
- EANR ≈ 0.18875 (rounded to four decimal places)
So, the annual expected net return, estimated using these assumptions, is approximately 0.1888 when rounded to four decimal places.
Q3 An investor collected data for the past 5 months. The estimated realized monthly net returns for those months are: R 1 = 6.59%, R 2 = 9.11%, R 3 = 9.69%, R 4 = -3% , R 5 = 5.6% Calculate the sample standard deviation of the realized monthly net returns. Round your intermediate steps to four decimals at least (if necessary). Input your answer with four decimals. Do not use percentage format! That is, 1.234%
should be input as 0.0123
To calculate the sample standard deviation of the realized monthly net returns, follow these steps:
1. Calculate the mean (average) of the returns.
2. Calculate the squared difference between each return and the mean.
3. Calculate the average of the squared differences.
4. Take the square root of the average squared difference.
Let's calculate it step by step:
Given monthly net returns:
R1 = 6.59% (0.0659)
R2 = 9.11% (0.0911)
R3 = 9.69% (0.0969)
R4 = -3% (-0.03)
R5 = 5.6% (0.056)
Step 1: Calculate the mean (average) of the returns:
Mean = (R1 + R2 + R3 + R4 + R5) / 5
Mean = (0.0659 + 0.0911 + 0.0969 - 0.03 + 0.056) / 5
Mean = 0.05678
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