Combining Portfolios to Increase RAROC - Is that Why Banks Always Merge?
Team Latte
Mar 07, 2005
Take two very ordinary, underperforming bank treasury & capital markets division. Suppose the treasury of bank A, which specializes in and trades G7 FX options generates US$9 million in annual profits on a capital of $100 million and has a volatility (of the G7 currencies in general and on a basket basis) of 15%. The treasury of another bank B, which specializes in and trades equity options and swaps generates US$10 million in profits on a capital of $80 million and has a volatility (of the basket of the instruments) of 25%.
Let us ask a purely theoretical question: Does it make sense to combine the two treasury divisions of these banks and one unit as a whole?
In practice this is ridiculous and non-workable but a far more practical and workable question is what if the treasury divisions were the entire banks themselves then would it be worthwhile to combine the two banks?
What are the benefits of combing these two operations? And why should it be done? The answer lies in the correlation and cuts through the heart of portfolio theory. Understanding how returns are measured against the risks taken to generate them is quintessential to not only understanding asset allocation models at the trader or fund manager level but also unraveling how banks, hedge funds and fund of funds operate in terms of capital allocation and trading strategies.
Let us approach the problem from a microcosm of two assets, A and B and a simple portfolio with a combination of A and B. Remember, A and B could eventually be two funds, two portfolios themselves or two banks.
It is a trivial observation in the markets that if two assets which are not perfectly positively correlated are combined then the non-systemic risk is diversified away. Under constant volatility assumption, if the two assets have perfect negative correlation then maximum risk diversification is achieved. Further, as long as the two (or more than two, in a general case) assets have less than perfect positive correlation risk will always be diversified away if they are combined in a portfolio.
Risk, which is defined and measure by the volatility of the asset or the asset return, is diversified away because of the mathematical property of non-additivity. Volatility, and therefore, risk, cannot be linearly added together. You cannot add the risk of an asset A and asset B simply as the sum of the two risks.
Risk(A + B) ≠ Risk(A) + Risk(B)
In fact, if asset A and asset B are added together then the sum of the risks would be given by:
Risk(Portfolio)=Risk(A + B) =  |
a d v e r t i s e m e n t
