# Covariance of assets with different probabilities for each scenario.

There are three assets given and for each asset there are three scenarios with their respective probabilities.

Asset 1:

$$\begin{array}{c|c|c|} & \text{Return} & \text{Probability} \\ \hline \text{Scenario 1} & 16 & 0.25 \\ \hline \text{Scenario 2} & 12 & 0.5 \\ \hline \text{Scenario 3} & 8 & 0.25 \\ \hline \end{array}$$

Asset 2:

$$\begin{array}{c|c|c|} & \text{Return} & \text{Probability} \\ \hline \text{Scenario 1} & 4 & 0.25 \\ \hline \text{Scenario 2} & 6 & 0.5 \\ \hline \text{Scenario 3} & 8 & 0.25 \\ \hline \end{array}$$

Asset 3:

$$\begin{array}{c|c|c|} & \text{Return} & \text{Probability} \\ \hline \text{Scenario 1} & 16 & 0.33 \\ \hline \text{Scenario 2} & 12 & 0.33 \\ \hline \text{Scenario 3} & 8 & 0.33 \\ \hline \end{array}$$

For assets 1 and 2 the scenarios mean Market Conditions: Good, Average, Poor, but for Asset 3 it is Rainfall: Plentiful, Average, Light. The exercises says "Assume there is no relationship between the amount of rainfall and the condition of the stock market". This is all the info given. I need to calculate covariances for Assets: Cov12, Cov13, Cov23. The Cov12 is straightforward and it gives a result of -4. The question is,how to treat Cov13 and Cov23? From the sentence about the relationship of the amount of rainfall with the stock market, i should assume that it is an independent variable, therefore, Cov=0? Some insights on this would be very much appreciated.

• You need the joint distributions to calculate covariance. The tables given are just the marginals. There should be more assumptions/information in the source material. – Lee David Chung Lin Feb 14 at 14:20
• Ok. So I re-read the exercise and for assets 1 and 2 the scenarios mean Market Conditions: Good, Average, Poor, but for Asset 3 it is Rainfall: Plentiful, Average, Light. The exercises says "Assume there is no relationship between the amount of rainfall and the condition of the stock market". This is all the info given. – BlackAdder Feb 14 at 14:32