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Dynamic Strategies for Asset Allocation Four Dynamic Strategies : buy-and-hold; constant mix; constant-proportion portfolio insurance; and option-based portfolio insurance Payoff and Exposure diagrams

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dynamic strategies for asset allocation
Dynamic Strategies for Asset Allocation

Four Dynamic Strategies:

  • buy-and-hold;
  • constant mix;
  • constant-proportion portfolio insurance; and
  • option-based portfolio insurance
payoff and exposure diagrams
Payoff and Exposure diagrams
  • Payoff diagram of a given strategy relates to the portfolio performance over a certain period of time to the performance of the stock over the same period.
  • Exposure diagram relates to thedecision of the strategy.

Buy-and-Hold ($100)

Value of assets ($)

100% stocks

100% Bills

Value of stock mkt

Buy-and-hold strategy - an initial

strategy (say, 60/40 stocks/bills) that isbought and then held.

Payoff Diagram



Payoff Example of 60/40 stock/bill

buy-and-hold strategy

Value of assets ($)



value of stock mkt


Exposure diagram relates the dollars invested in stocks to total assets; it shows the decision rule.


Desired stock position ($)

slope=1 (100% in stocks)

100% in bills (slope=0)

Value of assets ($)


Exposure Diagram: 60/40 Stock/Bill Buy-and-Hold Strategy

Desired stock position ($)





Value of Assets ($)

constant mix strategies
constant-mix Strategies
  • It maintains an exposure to stocks that is constant proportion of wealth
  • Dynamic approaches -when the relative values of assets change, purchases and sales are required to return to the desired mix.
  • Consider a 60/40 stock/bills constant mix strategy (or $60 in stocks and $40 in bills for a total investment of $100).

Exposure Diagram for 60/40

constant-mix strategy

Desired stock position




Value of Assets


Suppose the rule is to set 10% threshold, i.e, rebalance after 10% increase or decrease in stock price.

For Example:Initial Change RebalanceSt. Mkt 100 90 90

Stocks 60 54 56.4

Bills 40 40 37.6total assets 100 94 94

Due to “change”

stock/tot. asset =54/94=57.4%

After rebalance (i.e. buy more $2.4 stocks), i.e.,

stock/total asset =56.4/94=60%


The general rule of constant-mix strategy is to buy stocks when theirprices are falling and to sell stocks

when they are rising.

Payoff Diagram of 60/40

constant mix strategy

Value of Assets




Value of stocks

when will constant mix outperform buy and hold strategy
When will Constant-mix outperform Buy-and-Hold Strategy?
  • Consider a case in which stocks fall from 100 to 90, the recover to 100. The market is flat, but it oscillates back and forth.
  • Buy-and-hold strategy - same
  • Constant-mix strategy will do better than the buy-and-hold because it buys more stocks as they falls. When shares later increases in prices, the more share purchased will enhance the return for the Constant-Mix Strategy
  • Other cases include: large volatility and price reversals.
constant proportion strategies
Constant-Proportion Strategies
  • Constant-proportion strategy takes the form:Dollars in stocks = m(Assets - Floor)where m is a fixed multiplier.
  • Three special cases:(1) If m >1, the strategy is called the constant-proportion portfolio insurance strategy (CPPI).(2) If m=1, floor= value of bills, this strategy is the buy-and-holdstrategy.(3) If 0<m<1, floor= 0, the strategy is the constant-mix strategy.

Exposure diagram for CPPI

Desired position in stocks





Value of assets

Dollars in stocks= 2(100-75) =$50Thus, the initial investment for CPPI is50/50 stock/bills mix.


Under the CPPI, when a stocks fall in price, say from $50 to $45, the total asset value will be $95 (=45+50).

The new appropriate stock position = 2(95-75) = $40, implying sale of $5 of stocks and investment of theproceeds in bills. If stock prices rise in value, stocks should be bought.CPPI strategy sells stocks as they fall and buy stocks as they rise in value.

In a bull/bear market, CPPI will do well as it calls for buying/selling stocks as price rises/falls.

Price reversals hurt CPPI investorsbecause they sell on weakness only to see the market rebound and buy on strength only to see the market weaken.


Payoff Diagram for CPPI

value of assets

25/75 buy-and-hold

50/50 buy-and-hold

Value of stock market

concave and convex strategies
Concave and Convex Strategies
  • Strategies that “buy stocks as they fall, and sell stocks when they rise,” giving rise to concave payoff curves are called concave strategies.
  • Concave strategies do very poorly in flat in down or up market, but tend to do well in oscillating market. Eg: Constant-mix strategies.
  • Convex strategies are those “buy stocks when they rise or sell stocks when they falls”, e.g.. CPPI strategies
  • Convex strategies do well down or up market

Convex strategies represent thepurchase of portfolio insurance

because it has a floor value;

Concave strategies represent the sale of portfolio insurance.

Convex and concave strategies are

mirror images of each other.

When a portfolio combines a convex concave strategies, it results in a buy-and-hold strategy with a linear payoff diagram.

option based portfolio insurance
Option-based Portfolio Insurance
  • Option-based portfolio insurance (OBPI) strategies begin by specifying an investment horizon and a desired floor value at that horizon.
  • The value of the the floor is the present value value of the specified number discounted using the riskless rate.
  • Strategies involve buying of Tbills and call option. At maturity, the tbills ensure the floor value and option will have upside potential

Payoff Diagram for OBPI

value of assets

Value of stock market