Question

Discuss the basics of risk return analysis in the financial context and the statistical tools we use to analyze risk and return. Discuss how we can use this data to structure a portfolio and how we compute both portfolio return and portfolio risk and how diversification reduces overall portfolio risk.

Answer 1

To understand the basics of risk return analysis in the financial context we can take a very samll example,

There are three investors and each of them have equal amount of money to invest. The first investor, puts all his money in the bank where it is safe and there is close to zero risk. The second investor decides to put have his money in the bank and the other half in the stock market, so he is taking more risk than the first investor, but still wants to be conservative and not take the chance of losing all his money. The third investor, decides to put all her money in the stock market and is taking a huge risk of losing her money.

Now, if the return to the third investor and the first is the same, at different levels of risk, the third investor might also decide to play it safe and put her money in the bank. In that case, companies in the stock market wouldnt get any funding because they are not paying investors for the risk they under take.

Thus, it is fair to say that the rate of return increase with the amount of risk taken and if the risk is the same, then investing in what gives higher returns is the logical option. This can be seen through the efficient frontier graph given below:

The common statistical tools used to analyse risk and returns are:

- Standard deviation

- Beta values

- VaR or Value at risk: Under this there are various methods used such as:

1. Historical

2. Riskmetrics

3. GARCH, etc

- CVaR or Conditional value at risk

We can use this data to structure a portfolio, we compute portfolio returns by the follwing formula:

Where, weights are assigned to the stocks based on how many shares are held, for example if we hold 40 shares of stock A and 60 shares of stock B, the weight assigned to stock A would be 0.4 and 0.6 to stock B.

Portofolio risk is computed using the following formula:

where,

w1 = weight of first stock

w2 = weight of second stock

sigma1 = std deviation of first stock

sigma2 = std deviation of second stock

Cov 1,2 = covariance

For more than two stocks, matrix multiplication must be used.

All of this can be used to build a strong portfolio, by selecting stocks that have lower risk together than if held separately, this is possible if the stocks move in opposite directions in case of an event, this can be accounted for using covariance and corelation. It also can be seen that by having a diverse portfolio, events that may affect a certain sector or group, dont impact the entire portfolio. This further reduces risk. This can be seen from the following graph: