**Buy and Hold**

Investors who use a buy and hold strategy set their initial allocation weights and then do nothing. Such allocations are directly related to the market performance of risky assets, and using them implies that risk tolerance is directly related to wealth and market returns.

Consider a 60/40 split between stocks and the risk-free asset. As the stock market rises (falls), stocks represent a larger (smaller) weight in the portfolio and The risk-free asset provides a floor value. Returns are directly related to market performance in a linear relationship.

When markets are trending, buy and hold methods can perform well because the better performing assets get increasingly larger weights and poor-performing assets have less impact.

**Constant-mix**

Constant mix rebalancing is a dynamic process that requires rebalancing to the intial target allocation by trading whenever market conditions alter the ideal balance. The strategy ensures that the portfolio’s risk characteristics remain stable over time, consistent with a risk tolerance that varies proportionately to wealth.

Constant-mix strategies can be characterized as contrarian, as they sell the best-performing assets to buy the worst-performing. However, when markets are mean-reverting this will perform better than a buy and hold strategy. The shape of returns is concave – return increases at a decreasing rate in positive markets and decreases at an increasing rate in negative markets.

**Constant Proportion**

In a constant proportion strategy, the target allocation is a function of cushion, where cushion is the difference between the portfolio value and the floor value, and the allocation to risky assets is the product of the cushion and the proportion (m).Â A buy and hold strategy represents a special case in which m = 1. This strategy is consistent with having no risk tolerance if there is no cushion.

If m > 1, the strategy is known as constant proportion portfolio insurance, or CPPI. CPPI strategies buy more stocks when markets are rising and sell stocks as markets fall. The dynamic allocations also affect the floor value, as changing the weight of the risky asset necessitates an opposite-direction change in the floor value.

In strong bull markets, CPPI performs well by continually allocating more to stocks. In strong bear markets, CPPI avoids large losses by rapidly reducing the allocation to stocks. Such returns can be described as having a convex shape as the return increases at an increasing rate when market returns are positive and decreases at a decreasing weight when market returns are negative.

When markets are characterized by frequent reversals, the constant changes in allocation result in high transaction costs that erode performance.