Constant Proportion Portfolio Insurance

The Constant Proportion Portfolio Insurance ( CPPI ) is a dynamic portfolio hedging strategy.

History

The portfolio hedging strategies have their origins in the 1980s. They were due to long-lasting price losses on the national as well as international securities markets (eg the sharp rise in oil prices on the exchanges early 80s, of a continuing decline of 'absence). Due to the sustained upward movement in share prices on the stock exchanges in the 90s, hedging strategies have been pushed into the background. The idea of ​​portfolio insurance was especially through the work of Black and Perold (1982 ), as well as initiates Black and Jones ( 1987).

Basic concept

The goal of portfolio hedging strategies is to limit the risk of loss in the event of falling prices on the securities markets while allowing to participate in rising securities markets. Among the instruments of the CPPI strategy include risky financial assets ( shares) and risk-free fixed income investments (money market funds, certificates). Since this is a dynamic strategy, there will be a permanent restructuring of the portfolio between risky and risk-free investments throughout the period under consideration. In the CPPI strategy is assumed to be ex ante specified portfolio minimum.

To be as simple and comprehensible manner complex issues of the basic concept of the CPPI strategy is based on the following assumptions:

• On the market is trading at dividend-paying stocks.
• There is no way to take debt.
• There are no short sales allowed.
• It is possible to buy any number of securities (any divisibility ).
• In the market, there is a constant interest rate throughout the investment period.

Initial situation:

The values ​​of a hedged with the CPPI strategy portfolios for the first three time points are shown in the following table. Initial situation is the time zero.

As the initial situation presented above it can be seen, the initial wealth is € 100,000. Consequently, the portfolio value is €. Floor in is the discount of at Portfolimindestwert and is calculated as follows:

Cushion or safety buffer is the difference between the current portfolio value () and floor (). This amount can be completely risk ( the total loss can be tolerated ) and yet the portfolio minimum value is guaranteed in time () due to the proportion in the riskless asset.

In the above calculation, the determination of Cushions is represented at the time. Based on the assumption that no short sales are allowed, the cushion can not be negative, ie it may be minimal zero.

The exposure is the amount that is invested in risk assets. This equity component is determined not only from the Cushion together, but is constant multiples of it, since the probability of the total share loss on a day or overnight is very low.

In applying this strategy, it is assumed that no loans may be included. In the case of credit limits the exposure is calculated as in the above formula, and determines with specific numerical values ​​for the time point. This represents the maximum percentage of the assets that can be invested in a risky asset. Thus you can create risky up to 100% ( ) of the assets.

The remaining assets will be designated as a reserve asset and is applied in risk-free securities. This amount is calculated as follows:

Thus, results in the following division of property at the time:

Equity weighting and risk-free share:

In the case of rising share price in this example is the stock return for the time ( ) 9.53%.

The stock return has been calculated as follows:

For period 1:

The development of risk-free investment of at:

Thus, the portfolio value is in:

Calculating the values ​​for the further time points is the same.

In the upper portion of the graph on the left the development of the CPPI portfolio ( white line), the share price (red line), the Cushions (light blue line ) and the Floors (yellow line) is shown. The lower portion of the graph is the percentage asset allocation of the high-risk (blue area ) and the risk -free investments refer ( red area). As the chart reveals, here's a rising stock price development was simulated. It is clear to see that almost throughout the investment period the market portfolio and the pure stock portfolio has a relation to the CPPI strategy higher value. This is because a portion of the assets invested in a risk-free investment, which generates a lower return compared to a risky investment with rising share prices. This distance can be controlled by the choice of a suitable multiplier, but with the proviso that the value of a pure stock portfolio is above the Floor. At the portfolio composition in the lower portion of the graphic you can see that the CPPI strategy is pro-cyclical and trend-following. That is, increases with rising share prices of equities in the portfolio and lowered in the case of falling prices. The stock price increase to such an extent that is greater than the portfolio value, the assets will be 100% invested in a risky asset. This is seen in the time points respectively.

Unlike other portfolio hedging strategies a permanent portfolio adapt to various factors such as stock markets, interest rates, volatility takes place at CPPI. However, it may be because of ongoing portfolio shifts lead to high transaction costs. When markets are rising opportunity costs because the CPPI strategy achieves relative to the market performance lower return. Only at a share ratio of 100% market movement is mapped one to one into the performance of the portfolio. The share price falls during the investment period so deep that the Cushion to zero falls and rises in the course again, can no longer benefit from this rise, which is also to be regarded as a disadvantage. Furthermore, it should be noted that the CPPI strategy is flexible and easy to handle. However, the use of this strategy is recommended only when markets are falling, as this has shown the simulation, especially when the price decline as long-lasting proves, such as in the days of the first oil crisis in 1973/74 and second oil crisis in 1979/80.