Final answer:
To calculate the expected return of a portfolio, one needs the individual expected returns of each investment, which were not provided. Similarly, without the expected returns and their variances or covariances, the variance or standard deviation of the portfolio cannot be calculated. For individual investments from a venture capitalist, expected values can be found using a probability distribution function, and it's noted that high-risk investments generally offer the potential for higher returns to compensate for the risk.
Step-by-step explanation:
The expected rate of return is a measure of the average expected profits from an investment over a defined period of time. Calculating the expected return of a portfolio involves multiplying the weight of each investment by its respective expected return and then summing the results. However, it is not clear from the student's question what the expected individual returns are for investments A, B, and C. Therefore, to answer the question about the expected return of the portfolio, specific expected returns for each investment would be necessary.
Risk is often quantified by the variance or standard deviation of the returns. Variance measures how far a set of numbers is spread out from their average value, with a higher variance indicating higher risk. The standard deviation is the square root of the variance and represents volatility or risk in the same terms as the expected return. However, without the actual numeric expected returns and the variances or covariances of the investments, one cannot calculate the variance or standard deviation of the portfolio.
Regarding the three investments put forth by the venture capitalist, we can find the expected value for the software company, hardware company, and biotech firm by using the probability distribution function (PDF), which will include the respective probabilities of each outcome and the associated profits.
Understanding that high-risk investments typically offer the potential for higher returns is crucial in making informed investment decisions. Investors generally expect higher returns to compensate for the increased risk they undertake. Conversely, a low-risk investment has more predictable outcomes and typically offers lower returns.