The majority of strategic asset allocation models do not address the rebalancing decision – the decision of what the investor does as time passes.

Rebalancing strategies
The term dynamic asset allocation relates to rebalancing strategies where the asset allocation decision depends on investment performance up until the rebalancing point. There are three basic types of rebalancing strategies:
q Buy-and-Hold
q Constant Mix (CM)
q Constant Proportion Portfolio Insurance (CPPI).
With Buy-and-Hold each asset is held to maturity and no decision on the asset allocation is made during each instrument’s life. With CM a fixed percentage mix of assets is maintained. This will involve selling assets after prices have risen and reinvesting in assets when prices have fallen. Often this rebalancing is carried out on a periodic basis ranging from monthly to annually. With CPPI both the absolute amount in each asset class and the relative mix of assets varies as a function of investment performance. More sophisticated rebalancing strategies are typically variants of these three archetypes.
CM is widely used by pension funds. Pension fund fiduciaries typically view the strategic asset allocation as the major risk decision. However, the rebalancing policy may be a more effective risk control tool than the asset allocation. For example, fiduciaries may have a certain risk budget in mind when they set the strategic asset allocation. Adverse market conditions may result in a loss equal to that risk budget. The question then arises whether the fiduciaries should renew the risk budget allowing further losses. In contrast, CPPI provides a cap on the losses that can occur.

Constant Proportion Portfolio Insurance (CPPI)
Consider a risky asset (eg, equities) and a risk free asset (eg, an asset that matches projected pension cash flows). Under CPPI the investor invests a fixed, discretionary amount in the risk free asset and the remainder of assets is invested according to CM between the risky and the risk-free asset (which may involve a partial short position in the risk-free asset). In theory, the value of assets will never fall below that of the fixed amount that was initially invested in the risk free asset.
The CPPI rebalancing rule is shown below, where St is the risky asset, m is a multiplicative factor, Pt is portfolio value and Ft is the floor portfolio value.
St = m.(Pt – Ft)
For example, where m is 4 and a fund is 110% solvent, the fund can have 40% allocated to risky assets.
A feature of CPPI is that the multiplicative factor m is closely related to the ‘riskiness’ of the risky asset. The ‘crash size’, the loss the investor can sustain on the risky asset, corresponds approximately to a negative return on the risky asset of 1/m, ie, a 25% loss on the 40% in equities returns the fund to 100% solvency.
Examples
Consider the performance of CPPI versus CM in three generic market environments. The implementation of CM targets a 60% allocation to the risky asset as does the CPPI.
Figure 1 considers a bear market. For CM we buy the risky asset to top its portfolio proportion back up to 60%. For CPPI we sell large amounts of the risky asset as the portfolio value approaches the value floor. The total return is better under CPPI than under CM but turnover is larger under CPPI.
Figure 2 considers a bull market. Performance is better and turnover higher under CPPI. Under CPPI we buy considerable amounts of the risky asset.
Figure 3 considers a cyclical market. Performance is now better under CM but turnover is larger under CPPI.
CPPI versus CM in continuous time
Figure 4 shows the portfolio value under frictionless continuous rebalancing after one year for CM versus CPPI. CM dominates in the area of highest probability, but CPPI dominates in the tails. CPPI has higher expected return than CM, which in fact is a general result.
CM, being a so-called concave strategy, accelerates portfolio value down through the value floor if the market trends down. The benefit of CPPI is obvious: A soft landing in bear-markets while allowing for participation when markets recover.
CPPI has traditionally been viewed as a strategy with downside protection but with lower expected return than CM. This is not an accurate description.
In continuous time CPPI not only reduces downside risk in targeting a certain asset mix over time; it also offers a higher expected return over the CM strategy with the same target allocation to risky assets.

Real-world issues
There are several challenges that confront an investor aspiring to put CPPI into practice. Portfolio turnover is higher with CPPI, and thereby transaction costs. These shouldn’t be much higher than 10bp on average before the expected return of CPPI falls below that of CM. Secondly, and related; the operational burden of doing CPPI physically should not be understated. There is a need for close monitoring and frequent trading since the crash risk is a real risk. Crash risk can for the physical investor come in two forms:
q Instantaneous jump in market prices
q Fast but continuous changes in market prices.
The only way of protecting against the first form of crash risk is to get an underwriter to take on the gap risk. Such protection comes with a cost, further reducing the expected return on a realistic CPPI-implementation. The second risk can be covered, even for the CPPI-investor, but only with fast and liquid trading with low transaction costs. The majority of portfolio insurance based hedge funds have become cash locked due to jumps, high transaction costs and illiquid markets.
For pension funds the risk-free asset would usually be some long duration asset. The ‘risk-free’ asset is thus not risk free, it is a volatile asset. This complicates the operational implementation further, although the bond-floor crash risk can be assessed up-front and hedged.
In practice there are two ways of adopting CPPI. One way is for the investor to trade physically himself. This would require low transaction costs, heavy usage of derivatives, especially crash risk protection, excellent market access, frequent trading and significant operational challenges. The other way is to outsource CPPI to an external underwriter. This would in general be the preferred solution for most funds.
Considering regulatory stress tests, the investor does not usually get credit for the risk reduction mechanisms in CPPI without an external underwriter holding the crash risk, and he therefore needs to hold reserves against such scenarios. If the investor implements CPPI through a third party who takes on crash risk, the investor can take the derivative hedge into account in his stress testing.
Bearing in mind the large-scale failure of CPPI-based strategies in US equities in 1987, one should be cautious. There are however some obvious benefits to CPPI over CM, especially if the investor cannot allow the value of assets to fall below certain levels; true for the insurance and parts of the pension industry.

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