Final answer:
To establish the optimal asset allocation and expected returns for the venture capitalist's options, probability distribution functions, and expected values are calculated for each investment. Risk assessment is performed by analyzing variances, and market volatility helps identify the safest and riskiest options. The investment with the highest expected value will typically have the highest expected return.
Step-by-step explanation:
Optimal Asset Allocation, Expected Returns, and Risk Assessment for Investments
To determine the optimal asset allocation and calculate expected returns for the venture capitalist's investments, we need to construct a probability distribution function (PDF) for each investment and then find the expected value.
For the software company, the expected value is calculated as (0.10 * 5,000,000) + (0.30 * 1,000,000) + (0.60 * -1,000,000).
For the hardware company, the expected value is (0.20 * 3,000,000) + (0.40 * 1,000,000) + (0.40 * -1,000,000).
For the biotech firm, the expected value is (0.10 * 6,000,000) + (0.70 * 0) + (0.20 * -1,000,000).
After calculating these values, we can assess the risk tolerance by examining the variance or standard deviation of each investment. The one with the lowest variance (considering the probabilities and variations in returns) will be the safest.
Moreover, market volatility affects investments and is an indicator for risk assessment. An investment with higher volatility is considered riskier than one with lower volatility.
Safest and Riskiest Investments
The investment with the highest probability of not losing money and with lower variations in returns is seen as the safest. Conversely, the investment with a high probability of large negative returns (losses) is perceived as the riskiest. Based on the calculated expected values and considering potential losses, the biotech firm shows the least volatility, thereby being potentially the safest, while the software company shows the most, which may make it the riskiest.
Highest Expected Return
The investment with the highest expected return, on average, will be the one with the largest positive expected value, once calculated in the steps above. This reflects the potential average profit over time.