Portfolio Variance, Covariance and Correlation

CFA Level I Quant
#1

Hi All,

To understand a lot of the complex ideas in CFA, I usually create my own example of “pseudo real life” and try and apply what I have learned.

I am having a problem that I can’t seem to figure out.

Here is the example set up:

A 2 asset portfolio setup.

I have 20 year returns of Small Caps and Bonds. I want to see what the Standard Deviation of the portfolio would be if I invest 60% in Small Caps and 40% in Bonds.

Small Caps mean return = 11.12% with a standard deviation of 18.79%. Bonds mean return = 5.35% with a standard dev of 3.53%.

This is the Covariance matrix I get :

Small Cap Variance: 0.035304 Bond Variance: 0.001249 CoVariance: 0.000342 (Calculated this way: 0.60*(11.12-6.67)+0.40*(5.35-2.14))

I am getting an expected return of 8.81% and a st. dev of portfolio to be 11.43%. Is that right?

Also, for correlation, when I have Excel calculate it based on 20 year history and using “correl” command, it is giving me -0.37. Doing it via formula manually from above covariance, I am getting a correlation of 0.05. Big difference there. I can understand some difference due to the weights vs. using Excel command on 20 year data…but that much?

Appreciate someone’s help. THis is good example for practice. If I have left out some key data, let me know.

#2

I don’t know where you’re getting 6.67 and 2.14, but your calculation of covariance is not correct.

#3

Not sure how you derive most of your figures.

For multiple assets in a portfolio, the returns of the assets are likely not independent from each other. You need to derive their expectations, variances and covariances from a joint probability table.

It will be helpful if you can go through this video to revise on the topic again to see where you have gone wrong.

[video:https://youtu.be/OwimgcnS2uM?list=PL5C4op9wSllgf5TRqZeM2K7QX6YxoqSLc&t=7m42s width:480 height:270]

#4

Thx. I will watch the video tonight after I get home.

The 6.67% and 2.14% are the expected returns based on 60%/40% weight.

For small caps, I am assuming that we get 11.12%. With the 60% weight, that makes the Expected Value of 6.67%. And same for bonds.

I think that is where my problem lies - I am struggling to figure out if I should be doing: (11.12-6.67) vs. (8.81-6.67) - The 8.81 being the portfolio expected value.

Hope that clarifies.