Business Context
BlueRiver Capital is comparing two short-term trading strategies and wants a junior analyst to quantify average return, volatility, and downside risk using a simple discrete return model.
Problem Statement
Use the return distributions below to compare the strategies. Determine which strategy has the higher expected daily return, which has higher variance, and the probability that each strategy loses more than 1.0% in a day.
Given Data
Daily return outcomes are modeled as discrete distributions:
| Strategy | Return Outcome | Probability |
|---|
| A | -2.0% | 0.10 |
| A | 0.5% | 0.60 |
| A | 2.0% | 0.30 |
| B | -4.0% | 0.20 |
| B | 1.0% | 0.50 |
| B | 3.5% | 0.30 |
Assume these probabilities are accurate and sum to 1 for each strategy.
Requirements
- Calculate the expected daily return for Strategy A and Strategy B.
- Calculate the variance and standard deviation of daily returns for both strategies.
- Compute the probability that each strategy has a daily loss greater than 1.0%.
- If the firm is risk-averse and prefers lower volatility when expected returns are similar, recommend one strategy.
- Briefly explain how variance, distributions, and probability help interpret financial data in this example.
Assumptions
- Returns are measured in decimal form for calculations.
- Outcomes are mutually exclusive and collectively exhaustive.
- This is a one-day model; ignore compounding and serial dependence across days.
