Question on portfolio management - CFA BANK

CFA Level I Portfolio Management
#1

An analyst has made the following return projections for each of three possible outcomes with an equal likelihood of occurence:

Asset outcome 1 outcome 2 outcome 3 exp return (all in %)

1 12 0 6 6

2 12 6 0 6

3 0 6 12 6

If the analysts contructs two asset portfolios that are equally weighted, which pair of assets provides the least amount of risk reduction.

I’ve read the forum and saw how people determine the perfectly negative correlation of asset 2 and 3 by looking at the opposing trends of asset 2 and 3. However, in this case, combination of asset 1 and 2 ( down, up ) vs (down, down) and combination of asset 1 and 3 (down, up) vs (up, up) seems to be the same. How did the question come up with the pair that provides the least amount of risk reduction (i.e - the highest correlated pair)

Is there a formula to calculate this? correlation = cov ab/std dev of asset 1 and std dev of asset 2.

How do we calculate this?

#2

Hi hwanginyeop!

Looking at the overall trends can be confusing. In this case, I strongly suggest using the correlation calculation method in HP12c (if this is your calculator):

For example, pair 1|2
12 ENTER 12 Σ+
0 ENTER 6 Σ+
6 ENTER 0 Σ+
6 ENTER 6 Σ+
Then, insert any number, press | g | + | x,r | and | x >< y |

The correlation between 1 and 2 is 0.5, which is the pair that provides the least amount of risk reduction (1|3 = -0.5 and 2|3 = -1.0)

Hope it helps. Thank you