Advances in Risk Management

32 INCORPORATING DIVERSIFICATION INTO RISK MANAGEMENT

Table 2.1 Asset payoffs at timeTin both

scenarios

Asset Heads Tails

Riskfree capital 1 1

Risky asset #1 4 − 2

Risky asset #2 0 2

Table 2.2 Payoffs at timeTin both sce-

narios for the unacceptable portfolioη

Portfolio Heads Tails

η=[1,1,0] 5 − 1

Table 2.3 Payoffs at timeTin both sce-

narios for theη∗ADEHportfolio

Acceptable portfolio – ADEH Heads Tails

η∗ADEH=[2,1,0] 60

Table 2.4Payoffs at time T in both

scenarios for theη∗portfolio

Optimal Portfolio – QP Heads Tails

η∗=[1.11,0.78,0.22] 4.22 0

The distinction between the riskfree asset and its risky counterparts
is not central to our proposed risk management framework. In contrast to
traditional portfolio allocation decisions, the important issue in our context
is the tradeoff between additional risk-free capital versus rebalancing the
risky assets. A portfolio’s rebalancing may include the purchase of options,
futures contracts, insurance or reducing the portfolio’s exposure to certain
troublesome assets.
For example, to comply with the regulator, suppose the firm is faced
with two choices; adding $1,000,000 in riskfree capital (lowering their
expected return) versus acquiring positions in forward/futures/swap con-
tracts (which are costless at initiation) or inexpensive out-of-the-money
options. Naturally, deviating from the existing asset allocation between the
risky assets is essential since maintaining its exact composition would be
clearly inefficient. Subsection 2.2.2 contains additional economic motivation
in favor of rebalancing.