A buy and hold strategy has been called a linear investment strategy because portfolio returns are a linear function of stock returns. The share purchases and sales involved in constant-mix and Constant proportion portfolio insurance (CPPI) strategies introduce nonlinearities in the relationship.

For constant-mix strategies, the relationship between portfolio returns and stock returns is concave; that is, portfolio return increases at a decreasing rate with positive stock returns and decreases at an increasing rate with negative stock returns.

In contrast, a Constant proportion portfolio insurance (CPPI) Buy and Hold strategy is convex. Portfolio return increases at an increasing rate with positive stock returns, and it decreases at a decreasing rate with negative stock returns. Concave and convex strategies graph as mirror images of each other on either side of a buy-and-hold strategy. Convex strategies represent the purchase of portfolio insurance, concave strategies the sale of portfolio insurance. That is, convex strategies dynamically establish a floor value while concave strategies provide or sell the liquidity to convex strategies.

**Summary of Linear Investment Buy and Hold Strategy**

Exhibit 11-9 summarizes the prior discussion of Perold-Sharpe analysis.

It is important to recognize that we have focused the discussion ofperformance in Exhibit 11-9 and the text on return performance, not risk (except to mention the downside risk protection in the Constant proportion portfolio insurance (CPPI) and stock/bills buy-and-hold strategies).

Finally, the appropriateness of buy and hold strategy, constant-mix, and constant-proportion portfolio insurance strategies for an investor depends on the investor's risk tolerance, the types of risk with which she is concerned (e.g., floor values or downside risk), and asset-class return expectations, as Example 11-9 illustrates.

**EXAMPLE 11-9 Strategies for Different Investors**

For each of the following cases, suggest the appropriate strategy:

1. Jonathan Hansen, 25 years old, has a risk tolerance that increases by 20 percent for each 20 percent increase in wealth. He wants to remain invested in equities at all times.

2. Elaine Cash has a $1 million portfolio split between stocks and money market instruments in a ratio of 70/30. Her risk tolerance increases more than proportionately with changes in wealth, and she wants to speculate on a flat market or moderate bull market.

3. Jeanne Roger has a €2 million portfolio. She does not want portfolio value to drop below €1 million but also does not want to incur the drag on returns of holding a large part of her portfolio in cash equivalents.

*Solution to Problem 1:* Given his proportional risk tolerance (constant relative risk tolerance) and desire to remain invested in equities at all times, a constant-mix strategy is appropriate for Hansen.

*Solution to Problem 2:* Her risk tolerance is greater than that of a constant-mix investor, yet Cash's forecasts include the possibility of a flat market in which CPPI would do poorly. A buy-and-hold strategy is appropriate for Cash.

*Solution to Problem 3:* The concern for downside risk suggests either a buy-and-hold strategy with €1 million in cash equivalents as a floor or dynamically providing the floor with a CPPI strategy. The buy-and-hold strategy would incur the greater cash drag, so the Constant proportion portfolio insurance (CPPI) strategy is appropriate.

Loading

o
Microsoft
47.66
▲0.14 (0.29%)

o
Google
516.35
▲5.25 (1.03%)

o
BRE
0.00
(%)

o
Yahoo
50.88
▼0.03 (-0.06%)

## CAPITAL MARKET EXPECTATION TOOLS. SurveyThe survey method of expectations setting involves asking a group of experts for their expectations and using the responses in capital market formulation. If the group queried and providing responses is fairly stable, the analyst in effect has a panel of experts and the approach can be called a panel me... Tuesday, 17 May 2011 |

## Emerging Market DebtEmerging markets comprise those nations whose economies are considered to be developing and are usually taken to include Latin America, Eastern Europe, Africa, Russia, the Middle East, and Asia excluding Japan. Emerging market debt (EMD) includes sovereign bonds (bonds issued by a national government) as well as debt securities issued ... Friday, 20 May 2011 |

## Real Estate Market. Types of Real EstateAs one of the earliest of the traditional alternative investments, real estate plays an important role in institutional and individual investor portfolios internationally. The focus of our discussion is equity investments in real estate (covered in the definition given earlier).... Wednesday, 25 May 2011 |

## Long-Short PortfolioWhereas style investing is concerned with portfolio characteristics (low P/E, high earnings growth, etc.), long—short investing focuses on a constraint. Essentially, many investors face an investment policy and/or regulatory constraint against selling short stocks. Indeed, the constraint is so common and pervasive that many investors do not even recognize it ... Tuesday, 24 May 2011 |