CPPI: portfolio insurance with cushion, floor and multiplier

In depth11 min read · 12 sources

CPPI (constant proportion portfolio insurance) is a portfolio insurance strategy with a simple rule: above a lower limit, the floor, there is a cushion, and a fixed multiple of it is invested in equities. When prices rise, the equity share grows; when they fall, it is reduced until, in the extreme case, everything is held safely. Here you will learn how the rule works, when it helps, when it hurts and what the 1987 crash has to do with it.

The idea of portfolio insurance

Many investors want to profit from the stock market but under no circumstances suffer a certain loss, for example because the money will be needed for a flat in a few years. Portfolio insurance promises both: on the downside, the value is protected at a lower limit, and on the upside, part of the potential remains open. Leland (1980) asked early on which investors such a profile is actually worthwhile for, because the protection is not free.

There are two families of such strategies. Option-based portfolio insurance (OBPI) combines equities with a put or a safe asset with a call. Instead of buying options, you can also replicate them: Rubinstein and Leland (1981) showed that an option can be replicated by continuously adjusted positions in equities and cash. The second family does without option prices: CPPI, a fixed rule that only knows the distance to the lower limit.

How CPPI works: floor, cushion, multiplier

You set two numbers. The floor is the value that should not be undercut, for example 80% of the starting capital. The multiplier m determines how aggressively the cushion is used. Black and Jones (1987) described the rule as a simplified form of portfolio insurance:

The rule acts like leverage on the cushion. With m = 1, exactly the cushion is in equities and the floor is in the safe part. That is buy and hold, because no rebalancing is ever needed as long as the floor grows at the safe interest rate. Only with m above 1 does the strategy become dynamic: it buys after gains and sells after losses. A higher floor makes the cushion smaller and the equity share lower; a higher multiplier makes it larger.

Convex profile: trends versus zigzag

Perold and Sharpe (1988) classified rebalancing rules by their payoff profile. Buy and hold moves linearly with the stock market. A constant mix, i.e. classic rebalancing, buys after losses and sells after gains; its profile is concave. Portfolio insurance such as CPPI does the opposite, and its profile is convex.

The price for this: in markets without a clear direction that swing back and forth, CPPI does worse. The table shows three paths over two periods, with the same assumptions as above. The constant mix and buy and hold start with the same 80/20 split.

After the first period, CPPI is 100% in equities in the uptrend but only 52.2% in the downtrend. Both times it ends up ahead. In the zigzag, on the other hand, it loses, while the constant mix makes money. Whether CPPI pays off therefore depends on whether markets tend to trend or to reverse. More on trend rules in the article trend following.

For advanced readers: CPPI in continuous time

The theory of the strategy was worked out by Black and Perold (1992). If you assume that the share price fluctuates without jumps (geometric Brownian motion with volatility σ), that rebalancing is continuous, that no upper limit applies and that the floor grows at the safe interest rate r, the cushion follows a simple formula:

Two things are contained in it. First, the cushion depends on the m-th power of the price. That is where the convex, option-like profile comes from. Second, volatility eats into the cushion, by the factor m × (m − 1) / 2: the higher the multiplier, the more expensive a market that fluctuates a lot and ends up going nowhere.

Variants: TIPP, lock-in and guarantee periods

With a fixed floor, CPPI only protects the starting capital, not the gains. TIPP (time invariant portfolio protection), following Estep and Kritzman (1988), therefore ratchets the floor up: it is always a fixed share, e.g. 80%, of the highest portfolio value so far and never falls. Brennan and Schwartz (1988) described the whole class of such time-invariant insurance strategies that do without a fixed end date.

• TIPP: new high at 12,000 → floor 9,600. Part of the gains is then protected, but the cushion is smaller and the equity share falls.
• Lock-in in steps: the floor only jumps once the value has risen by one step since the last time, e.g. 10%. In between, more cushion remains for equities.
• Guarantee period: after a few years, a new period begins with a floor based on the value at that time.
• Growing floor: if the floor rises with the interest rate, an amount can be secured for an end date. If the entire starting capital is to be protected, the floor starts at its present value. When interest rates are low, this is close to the starting capital, and there is hardly any cushion left.

All variants trade protection for participation: the more closely the floor follows the portfolio, the more often the strategy enters a recovery with few equities after a decline.

Gap risk and cash lock

In theory, the value never falls below the floor, because the rule sells in time. In practice, trading only happens at certain points in time, and prices jump. Cont and Tankov (2009) show that with continuous trading and no jumps, CPPI has no risk of losses below the floor, but in real markets this risk is not negligible and grows with the multiplier. If the stock market falls by more than 1/m between two trading dates, the cushion is gone.

After such a fall, everything is in the safe part. If the floor is fixed, the safe part first has to lift the value back above the floor before equities return. If the floor grows with the interest rate, the strategy can hardly get out under its own steam. This state without equities is called a cash lock: the lower limit has held, but the recovery takes place without you. The pattern is reminiscent of sequence risk, because the timing of the slump determines the outcome.

OBPI versus CPPI

Both families aim to protect a lower limit, but they do it differently. Bertrand and Prigent (2002) compare them in detail; the main differences:

A purchased put option is expensive on average, because protection usually costs more than it pays out (see protective put). CPPI pays no premium but pays in other ways: with losses in the zigzag and with the risk of a cash lock.

1987: portfolio insurance in the crash

In the years before 1987, US investment firms offered portfolio insurance as a new product, and it became very popular. On October 19, 1987, “Black Monday”, the Dow Jones Industrial Average fell by 22.6%, or 508 points. According to Bernhardt and Eckblad (2013), the insurance relied heavily on options and derivatives and accelerated the crash, because initial losses triggered further rounds of selling.

Leland (1988), one of the early authors on portfolio insurance, sees it differently: the chaotic market conditions did make the insurance more expensive than usual, but it continued to provide substantial protection. In his view, it did not contribute significantly to the slide; the decisive factor was a lack of liquidity. How such strategies feed back into the market is examined by Brennan and Schwartz (1989) in an equilibrium model: they calculate how the risk premium, the cost of insurance, market volatility and interest rates change with the insured share of wealth.

For private investors, one lesson remains: a rule that many follow at the same time sells in the same minutes, precisely when buyers are missing. A single portfolio does not move the market, but it bears the gap risk just the same.

Costs, taxes and practice

• Review dates: frequent reviews reduce gap risk but increase turnover and costs. A tolerance band that has to be breached before any trading takes place saves many small reallocations.
• Trading costs: every reallocation costs spread and fees. They shrink the cushion and with it the future equity share.
• Taxes: in a taxable account, every sale at a gain triggers tax; the tax is then missing from the cushion. A rule that reallocates frequently sells more often than buy and hold.
• Choosing m and the floor: a high multiplier captures more of the upswing and is more vulnerable to jumps. A high floor protects more and leaves less room for equities.
• What CPPI is suitable for: a hard loss limit at a point in time, not a return booster. If you only want to dampen volatility, a lower fixed equity share achieves that more simply and without a cash lock.

It is also important to be clear about what the floor is not: a guarantee. It is a calculation variable of the rule. A real guarantee can only be given by someone who stands behind it. Then their creditworthiness counts.

How Portfolio Lab calculates it

On the CPPI page, you choose an equity part (a portfolio from the grid, a ticker or an asset class), a bond part and a cash part. The defaults are m = 4, a fixed floor of 80% of the starting value, review dates at month-end, a tolerance band of 5% and trading costs of 0.1% of each amount traded. Rebalancing between the parts can be stretched out to annually; portfolios from the grid get their own rebalancing as in the backtest, from none through monthly to annually or with a tolerance band. The floor can stay fixed or grow with interest and be ratcheted up via TIPP or lock-in; in addition, there are guarantee periods and a leverage limit. The page compares CPPI with a constant mix based on its starting split, with buy and hold of the equity part and with a bond benchmark made up of the bond and cash parts, and it counts floor breaches and periods without equities. The details are in the methodology.

This article explains a method; it is not investment or tax advice. Worked examples are simplified and rounded. All terms in the glossary.