Rebalancing / Perold-Sharpe Analysis / CPPI Strategy

CFA Level III Portfolio Management
#1

Volume 6 Page 94-95

Target Investment in stocks = m x (Portfolio Value - Floor Value)

“When stocks are trending down, the allocation to stocks decreases more than 1:1 with the decrease in value to stocks.”

“The CPPI strategy is just the opposite of the constant-mix strategy in using liquidity and being momentum oriented.”

Anyone find the formula to be inconsistent with the concept of a CPPI strategy? I understand that m is greater than 1 to relfect the fact that this is a momentum strategy - given an up move, the equity allocation value increases and the manager decides to increase the sensitivity to the stock market even more (hence, m > 1) in anticipation of another up move - but to me the formula seems to suggest that we buy stocks in a bear market which is a contrarian strategy not a momentum strategy.

If we invest £100 and hold a 60/40 stock/bond portfolio and the stock market moves down 20%, we now have a 55/45 stock/bond portfolio with the value of stocks being £48 - the cushion is £48. Based on the formula, we should increase the value of the cushion since m > 1. This entails buying stocks when we anticipate a further drop in the market (taking a momentum perspective), which doesnt make sense.

What I’d like to think they’re trying to say is that given the performance of a stock market, m is the multiplier by which adjust the cushion value, so if the market drops 20% and m = 1.1, the value of the allocation to equities should be reduced to a lower amount than £48 in anticipation of further down moves.

Another question, anyone kow what benchmark they’re referring to in the table in Exhbit 9. In an up-market for example, Buy and Hold “outperforms”, but I’m not clear of what it outperformed. All I know is that CPPI > Buy and Hold > Constant Mix in an up-market and a down-market whereas Constant Mix > Buy and Hold > CPPI in flat a flat market.

Thanks in advance.

#2

Incorrect as written: Market goes down - Floor value is fixed. Portfolio value goes down. So you would sell stocks.

For part 2 you need to get to a value for slope coefficient and a value for floor. Say 40 is the floor. and 1.2 is the slope coefficient. [You do not want investment to fall below 40].

Equity then = 1.2 ( 100 - 40 ) = 72. and cash = 100 - 72 = 28

Market falls 10% -> Equity now falls to 72 * 0.9 = 64.8

Portfolio = 64.8 stock, 28 Cash -> total = 92.8

Appropriate level of stock for this position is 1.2 * (92.8 - 40) = 63.36 --> so you sell 64.8 - 63.36 = 1.44 of stock and final rebalanced position = 63.36 stock, 28+1.44 = 29.44 cash for a position of 92.8

#3

Ok I see where I’m wrong, I think. I was assuming the investment in bonds was the floor.

But one thing I don’t get still is that in the book it says that a buy and hold strategy is established with a fixed investment in bills, by contrast in a CPPI strategy it is established dynamically.

So I take this to mean that in a buy and hold, the investment in bills sets the floor. Can you explain what is meant by “established dynamically” for CPPI?

Thanks for the help.

#4

the cash depends on how much the floor is - and the portfolio value.

as above == Stock = 1.2 (100-40) = 72, so Cash = 28.