What happens to Portfolio Protection (esp. CPPI) under Transaction Costs and Financial Transaction Tax?

· Trading Strategies
Authors

One of the most popular portfolio protection trading strategies is the Constant Proportion Portfolio Insurance (CPPI). This strategy maximizes the exposure in stock at each rebalancing time while  ensuring that the portfolio level never drops under the so-called floor.

Modeling Financial Transaction Tax

The currently proposed financial transaction tax is nothing else than a proportional transaction cost. The proposed value for the EU (especially France) is 0.1% for stocks and 0.01% for derivatives. In the following, we will denote this cost factor by alpha.

Traditional CPPI – no transaction costs

Using ThetaML, the CPPI strategy is easily defined. For simplicity, we leave out the interest-rate since currently, it is about zero anyways:

```model CPPI
import S "Stock price process"
import m "Multiplier"
import F "Bond floor"
import Pi_0 "Initial Portfolio value"
import T "Maturity time"
import n "Number of time steps"
export Pi "Portfolio value in EUR"

d = (m * (100-F))/S
Pi = Pi_0

loop n
S_old = S
% Let time pass for a time-step
Theta T/n

Pi = Pi + d*(S-S_old)
d = max( 0,(m*(Pi-F))/S )
end
end
```

CPPI and Transaction Costs

Since the Financial Transaction Tax is nothing else than proportional transaction cost, we can just decrease the portfolio after each rebalancing by transaction costs factor alpha times change in stock position.

That means we can write:

```model CPPI
import S "Stock price process"
import m "Multiplier"
import F "Bond floor"
import Pi_0 "Initial Portfolio value"
import T "Maturity time"
import n "Number of time steps"
import alpha "Proportional transaction costs"
export Pi "Portfolio value in EUR"

d = (m * (100-F))/S
Pi = Pi_0

loop n
S_old = S

% Let time pass for a time-step
Theta T/n

Pi = Pi + d*(S-S_old)
d_old = d
d = max( 0,(m*(Pi-F))/S )

% Reduce portfolio value by transaction costs
Pi = Pi - abs(alpha * (d-d_old) * S)
end
end
```

Sample Case

Let’s consider a specific case of a CPPI strategy:

```  m "Multiplier"                         = 5
F "Bond floor"                         = 8000
Pi_0 "Initial Portfolio value"         = 10000
T "Maturity time"                      = 10 (10 years)
n "Number of time steps"               = 250 * 10 (daily)
alpha "Proportional transaction costs" = 0.001 (0.1%)
```

and a market model with zero interest-rate and a geometric brownian motion with 20% volatility as stock price process.

That means, we look at a 10 year CPPI strategy with daily rebalancing and 10.000 EUR initial investment.

Using Theta Suite to evaluate ThetaML by Monte Carlo Simulation -without transaction costs- we get

CPPI without transaction costs presented as quantiles of 10000 simulated Monte-Carlo paths.

• Mean: EUR 27,096
• Median: EUR 8,186

We can see that without transaction costs, there is a 2.5% chance of making EUR 100,000  and more from the initial EUR 10,000 portfolio. But, about 50% of the portfolios lose the whole stock exposure and fall on the EUR 8,000 guarantee level (Bond Floor).

With transaction costs we get

CPPI with 0.1% financial transaction tax presented as quantiles of 10000 simulated Monte-Carlo paths.

• Mean: EUR 19,526 (-28%)
• Median: EUR 8,111 (-0.2%)

In the graph above we can see that with a financial transaction tax of 0.1% per trade, the 2.5% of the best paths earn about EUR 50,000 and more. This is half of what this strategy makes without this tax. The sample mean is down 28% and the median is almost unchanged. Consequently, the up-side potential of this CPPI strategy is hit dramatically by a 0.1% financial transaction tax.

CPPI and Exchange Traded Funds

Last week, I attended an interesting seminar by Phillipe Bertrand comparing CPPI and Leveraged Exchange Traded Funds (LETF). His slides are available here. He shows that CPPI and LETFs can be very similar and some deliver almost the same returns. I suspect that the reduced upside potential of the CPPI strategy will also hit the Leveraged Exchange Traded Funds. But, I leave the analysis to you, the reader: It is not hard to model LETFs with transaction costs.

Conclusion

The introduction of a financial transaction tax will hit the up-side potential of constant proportional portfolio insurance strategies considerably. In the presented case, the best 2.5% of the simulations will earn only about half after the introduction of this tax resp. transaction costs. This case can be seen as somewhat extreme since the presented strategy with a multiplier of 5 and daily rebalancing over 10 years is very aggressive. But, it shows that a portfolio protection which is desirable for most investors can be hit dramatically by the introduction of a financial transaction tax.

6 Comments

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1. Soeren Gerlach

Hi Andreas,

as I was just working recently in Munich on a CPPI-product on the IT side implementation your study shows exactly what has been discussed internally many times: The amount of fees seem to have a major impact on the overall performance, possibly even negating the possitive effect of the products “I” feature… The product setup was kind of portfolio management using a CPPI strategy, where the porfolio is built mainly from ETFs. Additionally the client was sold a gap option to protect him on gap risk that would occur due to the lagged rebalancing:

– A yearly fee based on the NAV of the portfolio
– A yearly fee (option premium) for the gap option, based on the NAV of the porfolio
– hidden: Transaction costs for the ETF transactions
– hidden: ETF management fees
– hidden: Index underperformance costs because not market, but provider indices where used (e.g. like Deutsche Bank’s “dbIQ” index family)
– maybe hidden: Kickbacks with ETF providers for the bank because of the usage of certain ETFs (this of course is part of the ETF’s TER but would likely increase it slightly).

However, this were just IT side internal discussions. Presenting these questions to the businees never resulted in an answer. Obviously they were more interested in the fees, then the clients portfolio performance.
Personally after gaining the knowledge about all this, I would not recommend to buy such a product.

On the other hand we assumed, that the average portfolio would need a rebalancing only once or twice a month, so a daily rebalancing is way too much.

Best regards,
Sören

• Katarzyna

The qitseuon is how often should a person rebalance their portfolio and how should they do it specifically. Let’s lay some groundwork before we answer the qitseuon. To properly rebalance you must have your portfolio with a firm that can accommodate rebalancing at no cost. You must also have a diversified portfolio as well as a target stock and bond asset allocation that suits your situation. Concentrated, focused or individual stock portfolios are not meant to be rebalanced so don’t try it because it will lead to disaster.Rebalancing works in three dimensions. The first dimension and by far the most important is the ratio of stocks to bonds. Our research over the last 80 years using daily data shows that almost all the benefits from rebalancing are gained in the first dimension. This means that you should always be aware of the ratio of stocks to bonds in your portfolio. When one gets too far ahead of the other it is time to rebalance. The second dimension is the ratio of stock asset classes to other stock asset classes within the portfolio. The last and third dimension is the ratio of bond asset classes to other bond asset classes in the portfolio.The rest of this response will focus on how to rebalance in the first dimension or the stock to bond dimension. There are only three ways to rebalance. The first is rebalance based on frequency or time. You rebalance every 2 weeks or every month or every quarter or some other nonsense. Don’t do it. This form of rebalancing does not capture the true benefit from proper rebalancing. It does not maximize the objective of rebalancing which is to reduce risk based on a target allocation. The second is to do it once a year. I actually like this much better for individual investors since it is a once a year thing and dose not require constant supervision. The third and best method is formulaic rebalancing.Our rule of thumb is to rebalance whenever the ratio of stocks in the portfolio diverges from the target allocation by more than 10%. As an example, for a 50/50 portfolio whenever stocks are either 45% or 55% of the portfolio we rebalance. For a 60/40 portfolio whenever stocks are either 54% or 66% of the portfolio we rebalance. Please note that if you have a 100% stock or bond portfolio you can’t rebalance in the first dimension and you lose the effectiveness of rebalancing. It is an obvious point but important. It is one of the main reasons why you see very few portfolios with allocations in excess of 80% in stocks or with less than 40% in stocks.If you use our 10% band for rebalancing you will find you get a signal every 8-10 months. Some periods where the markets are volatile will give you frequent signals and others will have you go for long stretches where you do nothing. We prefer this dynamic method for rebalancing because it takes into consideration market volatility.Mechanically, we don’t reinvest our dividends or interest. This means that when we rebalance and sell an asset class we add this to our money market funds. We include money market funds as part of our bond allocation. This leads to two more qitseuons. If you must rebalance because your first dimension or ratio of stocks to bonds is outside of the target allocation band by 10% which asset classes do you sell and which do you buy.There are only three logical choices that you can make when selling or buying when you get a rebalancing signal. Number 1 You can sell and buy some of each so that the ratio of the stock and bond asset classes remains the same after rebalancing. Number 2 You can overweight towards the leading or best performing asset class or classes or overweight towards the lagging or worst performing asset class or classes. Number 3 You can rebalance everything back to the original asset allocation. It is important to recognize that at this point you are simply tweaking your portfolio. You are now in the second and third dimension but not the most important one. Rebalancing between stocks and bonds far exceeds the importance of individual stock or bond asset class rebalancing. For those that are curious stock asset classes have a persistency effect that means that winners keep winning and losers keep losing. . This means that you will make more money if you allocate all of your money to the asset class that is performing the best and raise money from the asset class that is performing the worst. I have not yet released a tale addressing this persistency effect so for now I suggest the reader simply go with alternative Number 3 and rebalance back to the original allocation.

2. andrnev

Hi,
The Prmia CPPI link does not work. Can the author please put up these slides in the article?

3. andrnev

Thanks Andreas.

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