Covariance Units

Calculate the covariance of the returns of Bedolf Corporation (Rb) with the returns on Zedock Corporation (Rz) using the following data:

Rb=30%, Rz=15% Probability = 0.25

Rb=15%, Rz=10% Probability = 0.50

Rb=10%, Rz=5% Probablity =0.25

E(Rz)=17.5% and E(Rb)=10%

My question is when doing the calculations with covariance, are you supposed to use percentages as they appear (i.e.15% or 10%) OR are we supposed to use them as actual numbers (i.e. 0.15 or 0.10)? And additionally, what are the units of covariance?

Note that I used the actual number convention (0.15 & 0.10) and got a covariance of 0.0025 while the book used the other convention (15 & 10) and gave an answer of 25. Are these answers equivalent?

Finance people constantly get the units on covariance (and variance) wrong. You’ve done it correctly: 0.0025. When they write 25, they’re ignoring two percent signs: the answer should be 25%² = 25 × 1/100 × 1/100 = 0.0025. Their answer is wrong; it’s too big by a factor of 10,000.

That said, you’re in their world, and they write the correct answer as 25. You’d better do that if you want to get these questions right. You don’t have to like it – I hate it – but you have to do it their way because it’s their party.

Picking up on S2000’s response - on the exam, they won’t give you both 25 and .0025 as potential answers (at least, I doubt they will). The issue of "15 vs .0015) is mostly frustrating when mapping back to the text’s answers.

Also, as long as you’re consistent with using 15 vs 15%, both methods will give you the same correlation coefficient - the decimals cancel out, and you’ll get the same correlation using either method.

Yeah I hope they don’t test us giving 25 and 0.0025 as different answers! Looks like I’ll have to suck it up and do it the way they’ve prescribed… Thanks for your input guys