Institutional Investor's Alpha Magazine - December 2007/January 2008 - (Page 53)

of any of the portfolio’s securities, because investment in the portable alpha does not require capital. It is selfﬁnancing because we sell short the securities we wish to underweight and use the proceeds to purchase the securities we wish to overweight. We can apply a portable alpha to any part of the portfolio, not just the asset class from which it emanates. Consider a situation in which we believe our stock manager is skilled but our bond manager is not, and we desire a balanced portfolio of stocks and bonds. Conventional wisdom dictates the following course of action. Fire our bond manager and index the bond component of our portfolio. Convert our active stock portfolio to an index fund. Instruct our stock manager to convert her stock holdings to a portable alpha and extend it to cover both the stock and bond components of our portfolio. Although many believe these transactions would improve portfolio efﬁciency, they provide no beneﬁt to our portfolio beyond what we could achieve by preserving the linkage of alpha and beta. Perhaps New York Yankees catcher Yogi Berra showed us the best way to think about portable alpha. When the pizza delivery man asked Yogi after a game if he wanted his pizza cut into four slices or eight slices, Yogi replied: “Cut it into eight slices. I’m feeling hungry tonight.” TO UNDERSTAND THE EQUIVALENCE OF FIXED and portable alpha, imagine a simple world where the entire investment opportunity set comprises a stock market with only two securities of equal size and a single government bond. The hypothetical annual returns over ten years of these securities are shown in Table 1. Averages appear in the bottom row. Let’s also assume that we wish to maintain a 60 percent allocation to stocks and a 40 percent allocation to bonds. Finally, let’s suppose our goal is to maximize our ending wealth by managing alpha. We implement a portable alpha strategy by allocating 60 percent of our capital to the stock index and 40 percent to the government bond. These allocations establish our chosen market exposures. We then calculate the exposures to each stock’s alpha that maximizes our portfolio’s ending wealth, which turn out to equal a –22.64 percent position in stock A’s alpha and a 109.45 percent position in stock B’s alpha. We derive these weights through optimization. No other weights would result in higher ending wealth or, equivalently, faster growth. We establish our negative position in stock A’s alpha by selling short stock A and purchasing an equal amount of the stock index. We establish our long position in stock B’s alpha by selling short the stock index and purchasing an equal amount of stock B. These positions, which collectively constitute our portable alpha, are self-ﬁnancing. If we invest $100 in this portable alpha strategy, our portfolio grows to $241.72 over the ten years. In this scenario no other portable alpha strategy combined with an underlying 60/40 passive exposure to stocks and bonds would generate more wealth. Note that we do not employ leverage in this portable alpha strategy. Nor do we wander from our target market exposure of 60 percent stocks and 40 percent bonds. We simply extend our active stock exposure beyond our portfolio’s 60 percent stock allocation to a net active stock exposure of 86.81 percent (109.45 percent minus 22.64 percent). Now let’s see if we can attain the same ending wealth without resorting to portable alpha. Instead, we will invest directly in stocks A and B — with their alphas ﬁxed to their underlying market returns — along with the government bond. Again we constrain our stock allocation to 60 percent and our bond allocation to 40 percent. It turns out that a short position in stock A equal to –36.05 percent and a long position in stock B equal to 96.05 percent for a net stock exposure of precisely 60 percent, along with a 40 percent exposure to the government bond, produces the same level of ending wealth, $241.72. We arrive at these numbers by employing the same optimization algorithm as we did with the portable alpha strategy, but we preclude investment in the stock index and the portable alphas. By preserving the linkage of alpha to its underlying market return — and without resorting to leverage or increasing exposure to the market component of stocks — we attain the same result as we do with the portable alpha strategy. This equivalence becomes transparent when we examine the underlying security exposures of the two strategies. Table 2 reveals that when we parse the index weights and portable alpha weights into their underlying security exposures, the Table 2: Parsing portable alpha In our hypothetical two-stock world, we can show that the net exposures to stocks A and B are identical to their weights for the ﬁ xed alpha strategy by breaking down the index weights and portable alpha weights into the underlying exposures of the securities. Exposure 60.00 percent stock index –22.64 percent stock A alpha –22.64 percent stock A 22.64 percent stock index 109.45 percent stock B alpha 109.45 percent stock B –109.45 percent stock index Net exposure Stock A 30.00% — –22.64 11.32 — — –54.73 –36.05 Stock B 30.00% — — 11.32 — 109.45 –54.73 96.05 Source: Mark Kritzman. DECEMBER 2007/JANUARY 2008 • INSTITUTIONAL INVESTOR’S ALPHA • 53

Table of Contents Feed for the Digital Edition of Institutional Investor's Alpha Magazine - December 2007/January 2008

Institutional Investor's Alpha Magazine - December 2007/January 2008 Contents Letter from the Editor Longs & Shorts Pension Corner: Liberal Returns The Good Guy: Inner-city MVP Cover Story: Marathon Men Interview: Rizk Management Profile: Living on Hostile Ground Profile: Buy and Hold In Theory: The Fallacy of Portable Alpha Strategies: Changing Course Alpha Bytes: Behind the Scenes Unhedged: Commentary: An Activist Alternative

Institutional Investor's Alpha Magazine - December 2007/January 2008

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