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sovereign bond yields declined due to the flight-to-quality response. Even though investors desired to rebalance, many managers of fixed-income funds, especially in convertible bonds or mortgage-backed securities, had restricted liquidity by suspending redemptions or implementing gates. Experienced investors noticed a tremendous opportunity to rebalance using the derivatives markets. When the S&P 500 Index traded above 1,400 in May 2008, the 10-year Treasury yielded 3.8 %. At the market low in March 2009, Treasury notes had rallied to a yield of 2.8 %, while the S&P 500 traded below 700. There was quite a window for rebalancing, as the S&P 500 was valued at below 900 from the end of November 2008 to the end of April 2009. Investors who sold 10-year Treasury note futures and bought futures on the S&P 500 at any time during late 2008 or early 2009 had a tremendous profit from the rebalancing trade. This was because by the end of 2009, Treasury yields had returned to 3.8 % while the S&P 500 had moved above 1,100, producing a profit of at least 24 % on the equity trade alone. Investors who kept their fixed-income funds intact while hedging the change in Treasury yields multiplied their profits as yield spreads declined from record levels in the spring to more normal levels by year-end.

      Those schooled in options theory may notice that rebalancing activity is simply a short strangle trade, where both out-of-the-money calls and puts are sold. If the investor is committed to reducing the equity allocation after prices have risen 10 %, it can make sense to sell index call options 10 % above the market. This brings discipline to the rebalancing process and allows the fund to earn income through the sale of options premium. This income can be either spent by the sponsor of the endowment or foundation fund or used to reduce the risk of the investment portfolio. Similarly, committing to buy equities after a 10 % decline could be implemented through the sale of equity index put options with a strike price 10 % below the current market level. The simultaneous sale of calls and puts at the same strike price is termed selling straddles, while selling out-of-the-money calls and puts at different strike prices is termed selling strangles. While this approach can earn significant options premium and bring discipline to the rebalancing process, it is not without risk. The greatest risk is when the market makes a move larger than 10 % in either direction. The sale of options guarantees that rebalancing will occur at the level of the strike price, while those without options hedges may be able to rebalance after the market has moved by 20 % to 30 %. Investors can reduce the risk of using options to rebalance by selling call spreads and put spreads rather than selling strangles. While the purchase of further out-of-the-money options reduces risk and opportunity costs, the net premium earned from the sale of spreads will be less than that earned for selling strangles. Of course, there can be significant fear or euphoria after such a move, and some managers may hesitate to rebalance due to the foibles understood by students of behavioral finance.

      Some endowments may employ internal tactical asset allocation (TAA) models or external asset managers offering TAA strategies. As opposed to strategic asset allocation, which regularly rebalances back to the long-term target weights, tactical asset allocation intentionally deviates from target weights in an attempt to earn excess returns or reduce portfolio risk. TAA models take a shorter-term view on asset classes, overweighting undervalued assets and underweighting overvalued assets. While the risk and return estimates underlying the strategic asset allocation are typically calculated for a 10- to 20-year period, the risk and return estimates used by tactical asset allocation are typically much shorter, often between one quarter and one year. Tactical models are most useful when markets are far from equilibrium, such as when stocks are expensive at 40 times earnings or when high-yield bond spreads are cheap at 8 % over sovereign debt. TAA models can employ valuation data, fundamental and macroeconomic data, price momentum data, or any combination of the three.

      A number of alternative investment styles employ TAA analysis. Managed futures funds focus on price momentum, while global macro funds more commonly analyze governmental actions to predict moves in fixed-income and currency markets. TAA funds may employ both methodologies but are different from managed futures and macro funds. First, managed futures and macro funds take both long and short positions and often employ leverage; TAA funds are typically long-only, unlevered funds. Second, TAA funds may reallocate assets across a small number of macro markets, whereas managed futures and global macro funds may have a much larger universe of potential investments.

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      1

      Hundreds of studies have attempted to determine if active managers outperform passive strategies. S&P Dow Jones Indices publishes SPIVA® U.S. Scorecard on a regular basis. It reports on the relative performance of U.S. mutual funds.

      2

      More detailed discussions of asset allocation processes can be found in Maginn et al. (2007) and Ang (2014).

      3

      For further details, see Maginn et al. (2007).

      4

      For a detailed discussion of strategic asset allocation, see Eychenne, Martinetti, and Roncalli (2011) and Eychenne and Roncalli (2011).

      5

      In a simple equilibrium model, the short-term real riskless rate is shown to equal the real growth in the economy minus a premium that depends on the volatility of the economy's real growth rate and the degree of

1

Hundreds of studies have attempted to determine if active managers outperform passive strategies. S&P Dow Jones Indices publishes SPIVA® U.S. Scorecard on a regular basis. It reports on the relative performance of U.S. mutual funds.

2

More detailed discussions of asset allocation processes can be found in Maginn et al. (2007) and Ang (2014).

3

For further details, see Maginn et al. (2007).

4

For a detailed discussion of strategic asset allocation, see Eychenne, Martinetti, and Roncalli (2011) and Eychenne and Roncalli (2011).

5

In a simple equilibrium model, the short-term real riskless rate is shown to equal the real growth in the economy minus a premium that depends on the volatility of the economy's real growth rate and the degree of risk aversion. See Cox, Ingersoll, and Ross (1985).

6

The problem is still a rather standard optimization program and can be solved using Solver from Excel or similar packages.

7

From linear regression and the CAPM we know that βNew = Cov[RP, RNew]/Var[Rp].

8

For the history and theory of TAA, see Lee (2000).

9

See Tokat, Wicas, and Stockton (2007).

10

It is related to the correlation between the recommended weight and the actual weights.

11

See Dahlquist and Harvey (2001); Silva (2006); Tokat, Wicas, and Stockton (2007); Van

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