The Infidelity Mutual Fund Projects Three Possible Outcomes

The Infidelity Mutual Fund Projects Three Possible Outcomes For Ne Q1. The infidelity mutual fund projects three possible outcomes for next year: weak performance (-5 percent), good performance (10 percent), and outstanding performance (30 percent). The good performance has a 50 percent chance of happening and is twice as likely as the other outcomes. What is the expected value?

Q2. An investment has the following range of outcomes and probabilities: Outcome Probability of outcomes 6% 0...20 Calculate the expected value and the standard deviation (round to two places after decimal point where necessary).

Q3. Compute the duration for the following data. Use a discount rate of 13 percent. Year cash flow 1 $1,000 b. Explain why the answer to part A is higher than the answer to problem 2. c. if in part A the discount rate were 10 percent instead of 13 percent, would duration be longer or shorter? You do not need to actually compute a value; merely indicate an answer based on the discussion material in the text.

Paper For Above instruction The analysis of investment outcomes and their implications is central to understanding financial decision-making. This paper addresses several key questions related to expected value calculations, the assessment of investment duration, and the impacts of changes in discount rates on duration. Each section discusses core concepts, applies relevant formulas, and interprets results in the context of investment strategies and risk management.

Expected Value of the Mutual Fund Outcomes The first question involves calculating the expected value (EV) of the potential outcomes for a mutual fund. The given outcomes are: weak performance at -5%, good performance at 10%, and outstanding performance at 30%. The probabilities are partially specified: the good performance has a 50% chance of occurring, and it is stated that this probability is twice as likely as each of the other outcomes. This implies that the probabilities of the weak and outstanding performances are equal, and each is half of 50%, i.e., 25%. Therefore, the probabilities are: Weak performance (-5%): 25% Good performance (10%): 50%

Outstanding performance (30%): 25% Using these probabilities, we calculate the expected value as follows: EV = (Probability of weak)(Outcome of weak) + (Probability of good)(Outcome of good) + (Probability of outstanding)(Outcome of outstanding) EV = (0.25)(-5%) + (0.50)(10%) + (0.25)(30%) EV = (0.25)(-0.05) + (0.50)(0.10) + (0.25)(0.30) EV = -0.0125 + 0.05 + 0.075 EV = 0.1125 or 11.25% Thus, the expected return for the mutual fund next year is approximately 11.25%, indicating an overall positive outlook based on the projected outcomes.

Expected Value and Standard Deviation of Investment Outcomes The second question presents a different set of outcomes with associated probabilities, although the exact probabilities are partially obscured. Assuming the range of outcomes is from 6% to 20% with specific probabilities assigned to these outcomes, the expected value (EV) and standard deviation (SD) provide insights into the risk and return characteristics of this investment.

Suppose the outcomes are at 6%, 10%, 15%, and 20%, with assigned probabilities summing to 1. For example, if the probabilities are 0.2, 0.3, 0.3, and 0.2 respectively, the EV is calculated as: EV = Σ (Outcome × Probability) EV = (0.06)(0.2) + (0.10)(0.3) + (0.15)(0.3) + (0.20)(0.2) EV = 0.012 + 0.03 + 0.045 + 0.04 = 0.127 or 12.7% Standard deviation measures the dispersion of outcomes around the expected value and is computed as: SD = √Σ [Probability × (Outcome - EV)^2] Calculating SD using the same assumptions yields a value that quantifies the investment's risk profile.

Exact computation depends on the specific probabilities assigned.

Calculating the Duration of a Cash Flow

The third section involves calculating the duration of a cash flow, which is a measure of the weighted average time until cash flows are received, discounted at a specific rate. Given a single cash flow of $1,000 in Year 1 and a discount rate of 13%, the duration formula is: Duration = Σ [t × PV of cash flow at time t] / Price of the bond For a single cash flow, this simplifies to: Duration = (Time × Present Value of cash flow) / Present value of cash flow The present value (PV) is computed as: PV = Cash flow / (1 + r)^t Substituting values, PV = 1000 / (1 + 0.13)^1 ≈ 885.84 Thus, Duration ≈ (1 × 885.84) / 885.84 = 1 year.

The higher the discount rate, the lower the present value of future cash flows, which affects the duration calculation.

Discussion on Duration and Discount Rate Changes Part b asks why the duration calculated in part A might be higher than in another problem. Typically, duration tends to decrease as the discount rate increases because higher rates diminish the present value of distant cash flows more significantly, effectively shortening the weighted average time.

Furthermore, if the discount rate in part A were to decrease from 13% to 10%, the present value of future cash flows would increase, leading to a longer duration. This inverse relationship is well-documented in bond analysis: lower discount rates extend duration because the cash flows are valued higher and contribute more to the weighted average time until receipt.

In sum, duration is sensitive to the discount rate used. As rates go down, duration lengthens, reflecting a longer weighted average period until cash flows are received. Conversely, increasing the rate shortens duration, highlighting the importance of understanding interest rate impacts on bond and investment durations within financial management.

Conclusion The investigation into these investment assessments reveals that expected values provide a critical measure

for predicting potential returns, while standard deviation offers insight into risk. Duration, on the other hand, captures the sensitivity of an investment's price to interest rate changes. Recognizing how discount rates influence duration is essential for effective portfolio management, particularly in environments with fluctuating interest rates. Financial analysts must leverage these metrics to balance risk and return, optimize investment timing, and adapt strategies to changing market conditions.

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