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Dynamic asset allocation

Dynamic asset allocation updates asset exposures through time. A CPPI and fixed-weight ledger shows why the same market gain can produce opposite trades.

Dynamic asset allocation is a policy for changing a portfolio’s asset-class exposures over time as specified inputs change. Those inputs may include wealth, market prices, estimated risk, forecasts or remaining investment horizon. The practical question is what the portfolio should hold after the next change, rather than just what mix to hold today.
It belongs to asset allocation, but describes a decision process rather than one particular mix. A mechanical rule can be dynamic without predicting returns. Nor does a changing observed weight prove a dynamic decision: stocks can become a larger share of a buy-and-hold account simply because their prices rise.
Terminology varies across practitioners and textbooks. Some use “dynamic” narrowly for portfolio insurance or for market timing. Here it covers policies that update exposures through time. Tactical asset allocation usually means temporary departures from a longer-run mix based on market views; it is not a synonym for every dynamic policy. A wealth-based protection rule can change exposure without any view that equities are cheap or expensive.

One policy buys; another sells

Consider an illustrative, unlevered version of constant-proportion portfolio insurance, or CPPI. It makes the dollar stock target a multiple of the portfolio’s cushion above a chosen floor. This is one example of dynamic allocation, not its definition.

Use synthetic USD values, a constant floor of USD 8,000 and multiplier three. Cash earns zero interest. There are no external cash flows, dividends, fees, taxes or trading costs. Stocks are marked first; the rule is then applied at a decision time, with trades executed at that same mark. For nonnegative wealth WtW_t, let EtE_t be the dollar amount targeted in stocks immediately after trading:

Et=min⁡{Wt,  3max⁡(Wt−8,000,0)}.E_t=\min\left\{W_t,\;3\max(W_t-8{,}000,0)\right\}.

The remaining Wt−EtW_t-E_t stays in cash. The outer minimum caps stock exposure at total wealth, so this example does not borrow. The inner maximum prevents a negative stock target below the floor.

At USD 10,000 of wealth, the cushion is USD 2,000: the rule allocates USD 6,000 to stocks and USD 4,000 to cash. Compare it with a policy that restores a fixed 60% stock / 40% cash target at each decision time. Their initial holdings agree.
Now let stocks rise 20% before the next decision. Stock holdings become USD 7,200; cash remains USD 4,000. Both accounts are worth USD 11,200 before trading. Their next trades differ:
Decision at the new markCPPI ruleFixed 60% stock target
Target stock value (USD)3(11,200−8,000)=9,6003(11{,}200-8{,}000)=9{,}6000.60(11,200)=6,7200.60(11{,}200)=6{,}720
Stock trade (USD; positive means buy)+2,400−480
Cash after the trade (USD)1,6004,480
Total wealth after the trade (USD)11,20011,200
Two synthetic USD accounts start with stocks 6,000 and cash 4,000. After stocks rise 20%, both have stocks 7,200, cash 4,000 and wealth 11,200. CPPI buys 2,400 to reach stocks 9,600 and cash 1,600; the fixed 60% policy sells 480 to reach stocks 6,720 and cash 4,480.
Two synthetic USD accounts start with stocks 6,000 and cash 4,000. After stocks rise 20%, both have stocks 7,200, cash 4,000 and wealth 11,200. CPPI buys 2,400 to reach stocks 9,600 and cash 1,600; the fixed 60% policy sells 480 to reach stocks 6,720 and cash 4,480.
Original synthetic decision-time ledger in USD. Cash return is zero; the floor is fixed at USD 8,000. Trades transfer value between stocks and cash at unchanged marks. Blue denotes stocks and pale blue cash; both post-trade bars have equal total wealth.
CPPI increases stock exposure because the gain expands its cushion. The fixed-weight rule trims stocks because the gain puts their weight above target. Both involve rebalancing; their objectives prescribe opposite orders. “Rebalance regularly” is therefore an incomplete investment policy. It needs a target rule as well as a schedule or trigger.
The Turnover and the Information Horizon lesson develops the distinction between passive weight drift and deliberate trading, then measures the turnover created by forecast revisions. The full lesson requires membership; a public preview is available.

A floor in the formula is not a guarantee

Return to the original USD 6,000 stock / USD 4,000 cash account. Suppose stocks instead fall 40% before the next opportunity to trade. Wealth becomes
6,000(1−0.40)+4,000=7,600.6{,}000(1-0.40)+4{,}000=7{,}600.

The account is already USD 400 below the chosen floor. Setting its next stock exposure to zero cannot reverse the loss. In this starting account, a loss of one-third on stocks uses up the entire USD 2,000 cushion; a larger loss between trades breaches it.

This is portfolio-insurance gap risk: prices can move farther than the cushion can absorb before the rule can act. Discrete trading, jumps and limited liquidity matter. A contractual guarantee would need separate terms and a party bearing the shortfall; the allocation rule alone supplies none.

Even without a breach, reaching the floor under this fixed-floor, zero-interest specification leaves the account entirely in cash with no cushion to restart stock investment. More generally, a dynamic policy must specify how floors, constraints and decision times evolve. Its results depend on the sequence of returns, execution and transaction costs, as well as the initial allocation. The word “dynamic” establishes neither superior returns nor lower risk.

Sources

  • André F. Perold and William F. Sharpe, “Dynamic Strategies for Asset Allocation”, Financial Analysts Journal 44(1), 1988, pp. 16–27. The publisher’s public abstract distinguishes explicit dynamic rules, constant-mix strategies and portfolio-insurance strategies. A university-hosted reprint is also available.
  • Sven Balder, Michael Brandl and Antje Mahayni, “Effectiveness of CPPI Strategies under Discrete-Time Trading”, working paper dated 21 April 2006. The authors’ abstract identifies floor breaches under trading restrictions as gap risk.
  • Edwin J. Elton, Martin J. Gruber, Stephen J. Brown and William N. Goetzmann, Modern Portfolio Theory and Investment Analysis, 9th edition, Wiley, 2014, Chapter 10, pp. 207–208, and Chapter 28, pp. 727–728. These passages show differing uses of “dynamic asset allocation” and distinguish changing mixes driven by forecasts from portfolio-insurance objectives. The ledger here is an original illustration.
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  • asset allocation
  • dynamic policy
  • cppi
  • rebalancing
  • gap risk
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