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 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 100
Payoff Example of 60/40 stock/bill buy-and-hold strategy Value of assets ($) slope=0.6 40 value of stock mkt
Exposure diagram relates the dollars invested in stocks to total assets; it shows the decision rule. Buy-and-Hold Desired stock position ($) slope=1 (100% in stocks) 100% in bills (slope=0) Value of assets ($)
Exposure Diagram: 60/40 Stock/Bill Buy-and-Hold Strategy Desired stock position ($) slope=1 60 40 100 Value of Assets ($)
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 60 slope=0.6 100 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 Buy-and-Hold constant-mix 40 Value of stocks
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 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 50 slope=m=2 75=floor 100 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 • 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 (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