Allocated capital and VAR

This is CFAI 2012 q 16. We are given the table: Equity Desk Fixed Income Desk Capital 200 100 Daily VAR 10 10 Monthly profit 25 15 Question asks for which is most likely accurate with regard to the fixed income and equity trading desks: A. The trading desks have the same risk budget. B. The combined daily VAR of the trading desks is less than SEK20 million. C. The fixed income desk generates better returns on its allocated capital given its VAR.

Answer says: B is correct because the trading desks engage in activities that are weakly correlated; therefore, a diversification benefit is experienced, and it would be reasonable to expect that the combined VAR of the two desks will be less than the sum of the VARs of the individual desks (SEK20 million).

1. How do we know there is a diversification benefit? 2. Why is C incorrect? Fixed income generates a better return given its allocated capital and VAR.

You probablity missed a part where it says the correlation between the units are less than one. So the total firm VAR should be less than summed VARs remember the std for two asset? If correlation equal one then the std = waited average of the std of the assets. Why not C. FI dep generate 15%return over 10% Var the other generate only 12.5% over 5% VAR

Okay so i understand the correlation part. But why not C? Fixed income department profit = return / capital = 15/100 = 15% Equity department profit = return / capital = 25/200 = 12.5%. Hence fixed income makes a higher profit as a % of capital?

treated as risk adjusted return. Profit adjusted for VAR per capital. FI 15/10/100=1.5 equity 12.5/10/200=2.5 . Got it ? Each has Same VAR but different capital. So you must see each VAR per capital.

Sorry i’m still unclear on this. Why does the fixed income desk generate better returns on its allocated capital given its VAR? Equity Desk Fixed Income Desk Capital 200 100 Daily VAR 10 10 Monthly profit 25 15

It doesn’t, which is why C is wrong.

It does not. This is why C was not “most likely accurate”

Equity generates 25 with 5% VAR/Capital (uses less percentage of VAR) ; while FI generates 15 with 10% VAR/Capital.

Okay i get the working out. VAR/Capital for equity: 10/200=5% VAR/Capital for fixed income: 10/100=10% What does uses less percentage of VAR mean? Are we saying that equity will lose less of capital, than fixed income. And hence why equity is a better investment?

as a percentage of capital - Equity has a lower VAR allocated when compared to Fixed Income.