An investment portfolio in Singapore specializes in airline...

An investment portfolio in Singapore specializes in airline stocks and contains two of them. One is Singapore Airlines (mean: 0.12 ; standard deviation: 0.02 ), and it accounts for $30 \%$ of the portfolio shares. The other airline present in the portfolio is AirAsia (mean: 0.25 ; standard deviation: 0.15 ), a higher-risk, higherreturn investment. a. What is the expected value and the standard deviation of the portfolio if the coefficient of correlation of the two stocks is 0.5 ? b. What will they be if the correlation is 0.2 instead?

An investment portfolio in Singapore specializes in airline stocks and contains two of them. One is Singapore Airlines (mean: 0.12 ; standard deviation: 0.02 ), and it accounts for $30 \%$ of the portfolio shares. The other airline present in the portfolio is AirAsia (mean: 0.25 ; standard deviation: 0.15 ), a higher-risk, higherreturn investment.
a. What is the expected value and the standard deviation of the portfolio if the coefficient of correlation of the two stocks is 0.5 ?
b. What will they be if the correlation is 0.2 instead?

Key Concepts

Asset Weighting in Portfolios

Asset weighting refers to the proportion of the total portfolio that is invested in each asset. These weights play a crucial role in determining both the overall expected return and the risk profile of the portfolio by controlling the influence of each asset's return and volatility on the portfolio's performance.

Correlation and Covariance

Correlation measures the strength and direction of the relationship between the returns of two assets, while covariance quantifies the degree to which two asset returns move together. In portfolio theory, the covariance is often derived from the product of the correlation coefficient and the standard deviations of the asset returns, influencing the overall portfolio risk.

Expected Portfolio Return

This concept involves calculating the overall return of a portfolio as the weighted average of the individual asset returns. Each asset's expected return is multiplied by its corresponding weight in the portfolio, and the sum of these products gives the total expected return, offering a forecast based on the asset allocations.

Portfolio Standard Deviation

This is a measure of the risk or volatility of a portfolio's return. It is determined by not only the individual standard deviations of each asset but also by how the assets interact with each other, typically calculated through a combination of the weighted variances and the covariances between the assets.

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