A payoff diagram in the context of the article by Period and Sharpe, is a graph of the relationship between total portfolio (asset) value on the vertical axis and stock market index value (performance of the risky asset class) on the horizontal axis. Simply put, it tells the investor the profit and loss of his or her entire portfolio in relationship to movement in the stock market.
For example, consider a buy-and-hold strategy that purchases a particular combination (e.g., 50%/50%) mix of a risky asset (stocks) and a risk free asset (bonds). The bond values are assumed constant and for simplicity do not even pay interest. The buy-and- hold strategy does not rebalance, so the stock position simply grows and shrinks linearly with the stock market as depicted below. The slope of the line depends on the original mix, but the relationship is linear regardless of initial mix
Buy & Hold
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| X
| X
| X
| X
| X
Total Portfolio
Value | X
| X
| X
|_X_____________________________________________________
Value of the Stock Market
Now consider a constant proportion strategy that sells stock in a rising market to maintain the desired mix and buys stock in a declining market similarly to maintain a desired mix.
The payoff diagram will demonstrate a concave relationship as indicated below:
Constant Mix
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| X
| X
| X
| X
| X
Total Portfolio
Value | X
| X
| X
|_______________________________________________________
Value of the Stock Market
Now consider a Constant-Proportion Portfolio Insurance (CPPI) strategy that buys stock in a rising market and sells stock in a declining market (to protect a floor value).
The payoff diagram will demonstrate a convex relationship as indicated below:
CPPI strategy
| X
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| X
| X
| X
| X
Total Portfolio
Value | X
| X
| X
X
|_______________________________________________________
Value of the Stock Market
Finally, consider an option-based portfolio insurance strategy that owns a constant stock position in a rising market and sells all stock if a lower floor is reached in a declining market (to protect a floor value). The payoff diagram will demonstrate a kinked but otherwise linear relationship similar to the traditional diagram of a call options and as indicated below:
Option-based portfolio insurance strategy that owns a constant stock position in a rising market and sells all stock if a lower floor is reached in a declining market
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| X
| X
| X
| X
|X X X X
Total Portfolio
Value |
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|
|_______________________________________________________
Value of the Stock Market
In summary, the key to the payoff diagrams is that they show the linearity, concavity, convexity and call-option-like relationships of the four strategies as reviewed above. These shapes are important in understanding behavior in trending versus reverting markets.
An exposure diagram in the context of the article by Period and Sharpe, is a graph of the relationship between desired stock position (amount of risk) on the vertical axis and total portfolio value on the horizontal axis. Simply put, it tells the investor the risk exposure of the portfolio in relationship to the total portfolio’s cumulative performance.
For example, consider a buy-and-hold strategy that purchases a particular combination (e.g., 50%/50%) mix of a risky asset (stocks) and a risk free asset (bonds). The bond values are assumes constant and for simplicity do not even pay interest. The buy-and- hold strategy does not rebalance, so the stock position simply grows and shrinks linearly with the stock market with a lower bound equal to the bond position as depicted below.
The location of the line on the horizontal axis depends on the original mix and bond position but is linear regardless of initial mix. The key to the diagram is that it has a moderate slope.
Buy & Hold
| X
| X
| X
| X
| X
| X
Portfolio’s Stock
Value | X
| X
| X
|_____________________________________________________
Value of the Total Portfolio
Now consider a constant proportion strategy that sells stock in a rising market to maintain the desired mix and buys stock in a declining market similarly to maintain a desired mix.
The key to the diagram is that it has a moderate slope.
Constant proportion strategy
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|
|
|
| X
| X
Portfolio’s Stock
Value | X
| X
| X
|_X___________________________________________________
Value of the Total Portfolio
Now consider a Constant-Proportion Portfolio Insurance (CPPI) strategy that buys stock in a rising market and sells stock in a declining market (to protect a floor value). The exposure diagram will demonstrate a steeply sloped relationship as indicated below:
CPPI strategy
| X
| X
| X
| X
| X
| X Portfolio’s
Stock
Value | X
| X
| X
|______________ X__________________________________
Value of the Total Portfolio
Finally, consider an option-based portfolio insurance strategy that owns a constant stock position in a rising market and sells all stock if a lower floor is reached in a declining market (to protect a floor value). The exposure diagram will demonstrate a steep and curved relationship as indicated below:
Option-based portfolio insurance strategy that owns a constant stock position in a rising market and sells all stock if a lower floor is reached in a declining market
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|
| X
| X
| X
| X
Portfolio’s Stock
Value | X
| X
| X
|__________________ __________X________________________
Value of the Total Portfolio