There are several risks related to the trend toward convergence. These include 1. Mismatch of liquidity provisions and investment skill sets,
2. Diversification (so that investors do not find themselves with one or two illiquid investments), and
3. Appropriate staffing to trade, finance, restructure and, if necessary, operate underlying investments.
The authors note that as hedge funds realize the impact that their capital can have on the management of public companies, excesses could arise but few high profile conflicts are anticipated. Hedge funds need to have appropriate staffing to operate underlying investments, if necessary, duties that have not traditionally fallen on a hedge fund manager’s modus operandi.
References
Anson, M.J.P. “Collateralized Fund Obligations: Intersection of Credit Derivative Market and Hedge Fund World.” Chapter 25 in Handbook of Alternative Assets, 2nd edition. Edited by Frank J. Fabozzi. John Wiley & Sons, 2006.
Mansour, A., and H. Nadji. “Performance Characteristics of Infrastructure Investments.” RREEF Research – A Member of the Deutsche Bank Group. August 2007.
Weistroffer, C. “Coping with Climate Change.” Deutsche Bank Research. November 15, 2007.
Amenc, N., W. Gehin, L. Martellini, and J.C. Meyfredi. “The Myths and Limits of Passive Hedge Fund Replication: A Critical Assessment of Existing Techniques.” Journal of Alternative Investments. Fall 2008.
Gonzalez-Heres, J., and K. Beinkampen. “The Convergence of Private Equity and Hedge Funds.”
Morgan Stanley’s Investment Management Journal. Vol. 2, No. 1, 2006.
T O P I C 8
Asset Allocation
M a i n P o i n t s
Comparing and contrasting buy-and-hold, constant mix, and constant- proportion portfolio insurance strategies
Applying a wealth allocation framework that accounts for various dimensions of risk and deriving an ideal asset allocation for an individual
Interpreting the term structure of futures prices, the components of futures returns for individual contracts, returns for portfolios constructed and rebalanced with various methods, and the implications of tactical asset allocation strategies using commodity futures contracts
Critically examining the methods of including global commercial real estate in a strategic asset allocation
1. Calculate the portfolio’s asset values after a given change in the equity value, using:
a. buy-and-hold.
Perold and Sharpe consider various rebalancing strategies between a risk free bond and the stock market (with interest rates set to zero for simplicity). There are three primary strategies discussed as summarized below:
Strategy Name Rebalancing in Up Market
Rebalancing in Down Market
Shape of Payoff v. Stock Market
Buy-and-hold None None Linear
Constant Mix Sell Stock Buy Stock Concave Constant Proportion
Portfolio Insurance Buy Stock Sell Stock Convex
Consider for example an investor with $100 starting value allocating all of the funds between two choices: risk free bonds (interest rate equals zero for simplicity) and a single risky portfolio (the stock market). Assume that the investor’s initial allocation is to put
$70 in stock and $30 in bonds. The stock market is indexed to 100.0
Under a buy-and-hold strategy there is no rebalancing. The “Up” panel below shows the value of the portfolio in an up market with the market index rising
10 points each period for three consecutive periods. The “Down” panel below shows the value of the portfolio in an analogous down market. Any funds used to purchase stocks come from bonds and vice versa.
“Up” Market Panel: Buy-and-hold:
Before Balance After Balance
Time Stock
Level Bonds Stocks Stock Bought(+)
or Sold (-) Bonds Stocks Total
0 100.0 30 70 0 30 70 100
1 110.0 30 77 0 30 77 107
2 120.0 30 84 0 30 84 114
3 130.0 30 91 0 30 91 121
“Down” Market Panel: Buy-and-Hold:
Before Balance After Balance
Time Stock
Level Bonds Stocks Stock Bought(+)
or Sold (-) Bonds Stocks Total
0 100.0 30 70 0 30 70 100
1 90.0 30 63 0 30 63 93
2 80.0 30 56 0 30 56 86
3 70.0 30 49 0 30 49 79
Note that there are no transactions since the strategy is buy and hold. Further note that the total value is linear – it changes by the same dollar amount for each equal dollar movement in the stock market. The value of the portfolio (last column on right) changes
$7 for each 10 point change in the stock market index when it is 70% initially invested in the stock market and there is no rebalancing.
b. constant mix.
Perold and Sharpe consider various rebalancing strategies between a risk free bond and the stock market (with interest rates set to zero for simplicity). There are three primary strategies discussed as summarized below:
Strategy Name Rebalancing in Up Market
Rebalancing in Down Market
Shape of Payoff v. Stock Market
Buy-and-hold None None Linear
Constant Mix Sell Stock Buy Stock Concave Constant Proportion
Portfolio Insurance Buy Stock Sell Stock Convex
Under a “Constant Mix” strategy there is periodic rebalancing such that the portfolio is returned to being, in this case, 70% stocks and 30% bonds. The “Up” panel below shows the value of the portfolio in an up market with the market index rising 10 points each period for three consecutive periods. The “Down” panel below shows the value of the portfolio in an analogous down market. Any funds used to purchase stocks come from bonds and vice versa.
“Up” Market Panel: Constant Mix:
Before Balance After Balance
Time Stock
Level Bonds Stocks Stock Bought(+)
or Sold (-) Bonds Stocks Total
0 100.0 30 70 0 30 70 100
1 110.0 30 77 -2.10 32.10 74.90 107.00
2 120.0 32.10 81.71 -2.04 34.14 79.67 113.81 3 130.0 34.14 86.31 -1.99 36.13 84.31 120.45
“Down” Market Panel: Constant Mix:
Before Balance After Balance
Time Stock
Level Bonds Stocks Stock Bought(+)
or Sold (-) Bonds Stocks Total
0 100.0 30 70 0 30 70 100
1 90.0 30 63 +2.10 27.90 65.10 93.00
2 80.0 27.90 57.87 +2.17 25.73 60.04 85.77
3 70.0 25.73 52.54 +2.25 23.48 54.78 78.26
The $2.10 sale of stocks (and purchase of bonds) in time period 1 of the “Up panel” is a rebalancing such that the new value of the portfolio ($107) remains 70% allocated to stocks. Stocks are sold as the stock market trends up to prevent “underweighting” in bonds. In the downward panel, stocks are purchased as the stock market trends down to prevent “underweighting” of stock.
Very importantly, note that the total value is non-linear – it changes by smaller dollar amounts for each equal upward dollar movement in the stock market. The value of the portfolio rises $7 for the first upward 10-point change in the stock market index but rises by only $6.81 for the second 10-point change (the rebalanced stock holding does not rise by $7 because the 10-point stock rise is a smaller percentage stock price rise than it was when the stock level was lower). Conversely, rebalancing to the stock market while it is falling produces larger losses than in previous periods or in the buy-and-hold strategy (note that each 10-point decline in the market index represents a higher percentage decline).
Viewed on a graph with total portfolio value on the vertical axis and stock market index values on the horizontal level, the Constant Mix strategy forms a concave shape. The buy-and-hold strategy forms a straight line.
c. constant-proportion portfolio insurance.
Perold and Sharpe consider various rebalancing strategies between a risk free bond and the stock market (with interest rates set to zero for simplicity). There are three primary strategies discussed as summarized below:
Strategy Name Rebalancing in Up Market
Rebalancing in Down Market
Shape of Payoff v. Stock Market
Buy-and-hold None None Linear
Constant Mix Sell Stock Buy Stock Concave Constant Proportion
Portfolio Insurance Buy Stock Sell Stock Convex
Under a “Constant-Proportion Portfolio Insurance” (CPPI) strategy the investor sets a floor value at which all risky investing terminates. Further, the investor increases risky assets holding when the market rises and decreases risky asset holdings when the market falls.
For example, consider that the investor sets a floor value of $50 but invests 150% of the total portfolio value in excess of this floor in stock. Thus, the investor starts with a total value of
$100 allocated $25 to bonds and $75 to stock. At the end of each period, the investor resets the stock allocation so that it is 150% of the excess, if any, by which the total portfolio exceeds the floor ($50). Any funds used to purchase stocks come from bonds and vice versa.
“Up” Market Panel: CPPI:
Before Balance After Balance
Time Stock
Level Bonds Stocks Stock Bought(+)
or Sold (-) Bonds Stocks Total
0 100.0 25 75 0 25 75 100
1 110.0 25 82.50 +3.75 21.25 86.25 107.50
2 120.0 21.25 94.09 +3.92 17.33 98.01 115.34 3 130.0 17.33 106.18 +4.08 13.25 110.26 123.51
“Down” Market Panel: CPPI:
Before Balance After Balance
Time Stock
Level Bonds Stocks Stock Bought(+)
or Sold (-) Bonds Stocks Total
0 100.0 25 75 0 25 75 100
1 90.0 25 67.50 -3.75 28.75 63.75 92.50
2 80.0 28.75 56.67 -3.54 32.29 53.13 85.42
3 70.0 32.29 46.49 -3.32 35.61 43.16 78.78
The $3.75 purchase of stocks (and sale of bonds) in time period 1 of the “Up panel” is a rebalancing such that the new allocation increases its “bet” on stocks. Stocks are bought as the stock market trends up to try to achieve massive gains. In the downward panel, stocks are aggressively sold as the stock market trends down to prevent larger losses and to insure that the floor value ($75) is protected.
Very importantly, note that the total value is non-linear – it changes by larger dollar amounts for each equal upward dollar movement in the stock market. The value of the portfolio rises $7.50 for the first upward 10-point change in the stock market index and rises $7.84 for the second 10-point change (since the strategy placed 150% of “profits” in stock). Conversely, rebalancing away from the stock market while it is falling produces smaller losses than in previous periods. Over the long-term, the floor should increase, so that the relationship between the initial floor and a floor at time “t” is
Ft =F0ert
where Ft, F0, r, and t are are the floor value of the portfolio at time t, the floor value at initiation of the strategy (t=0), the risk-free rate, and a time index.
At a given point in time, viewed on a graph with total portfolio value on the vertical axis and stock market index values on the horizontal level, the CPPI strategy forms a convex
shape. The buy-and-hold strategy forms a straight line and the constant mix strategy forms a concave shape.