1. Week 14 Portfolio Insurance

2. Portfolio Insurance (1) Recall that managers can use puts to keep a floor on their portfolio. However, puts can be very expensive (especially for out-of-the-money puts). In particular, we observed that the volatility that is used to price out-of-the-money puts appears very high relative to actual volatility. Also, using S&P 500 index puts to trade is always an approximation, as your portfolio may imperfectly correlated to the S&P 500. An alternative to using puts to hedge is to use a trading strategy called “portfolio insurance”. Portfolio insurance attempts to replicate a put by trading the underlying portfolio.

3. Main Idea behind Portfolio Insurance (2) Suppose your current NAV is 10. You want to ensure that your NAV does not fall below 9. One way to achieve this goal is to sell your portfolio as the market falls, so that you are completely into cash by the time your NAV has reduced to 9. Your trading strategy is to increase your cash position as the market declines (with a goal of 100% cash at a portfolio value of 9), and decrease your cash position as the market increases. This trading strategy is called “portfolio insurance”. Qt: how much do you buy/sell with market fluctuations?

4. Portfolio Insurance (3) To determine how much to buy or sell, you use the put’s delta (or hedge ratio) as a guide. Suppose the current NAV is 10.00, and you want to put a floor at $8.50. Instead of buying a put with strike, 8.50, you want to implement a portfolio insurance strategy. The delta or the hedge ratio of the put (from the Black-Scholes spreadsheet) of a strike of 8.50 is about 0.18. Thus, your initial position at a NAV of 10 will be 18% in cash, and 82% in your portfolio. You will change the weights as the price moves.

5. Portfolio Insurance (4) For different levels of the price you can figure out the level of cash from the Black-Scholes formula. For example, at a price of 10,9,8,7,6,5,4 your cash position will be 18%, 31%, 50%, 70%, 87%,97%, and 100% respectively. To figure out (approximately) the average price you receive on your portfolio, we can add up how much we sold at each price level. Let us assume that you sold your position at the average price between each price level. Thus, between the price of 9 and 8, we will assume that you sold 19% (0.5- 0.31) of your portfolio at an average price of 8.50.

6. Portfolio Insurance (5) We will assume that your initial position in cash at 0.18 can be achieved by selling part of your portfolio at its current price of $10.0, and that you liquidate completely at a price of 4.50. Average price = 10.00x0.18 + 9.50x(0.31- 0.18)+ 8.50x(0.5-0.31) + 7.50x(0.7-0.5) + 6.50x(0.87-0.7) + 5.50x(0.97-0.87) + 4.5x(1-0.97) = $7.94. Thus, your “portfolio insurance” strategy has resulted in a floor that is close to $8.50 (that you wanted to achieve).

7. Portfolio Insurance (6) What are the advantages/disadvantages of this strategy? A. Advantages: 1. You do not have to worry about finding an option on an index that is correlated with your portfolio. 2. May be cheaper than an option, if the out-of- money put is very expensive. 3. The transaction costs of trading the underlying stocks are lower than that of trading options.

8. Portfolio Insurance (6) B. Disadvantages: 1. It may fail precisely when you require it the most - when there is a big crash - as you may not be able to quickly sell at your average price. 2. Also, you are selling when the price is falling - if enough portfolio managers are selling, they will make the price fall even more, which will in turn trigger even greater selling! In fact, many regulators and the press blames portfolio insurance for causing/exacerbating the 1987 crash. Overall, it appears that puts and portfolio insurance strategies are complementary, but not perfect substitutes.

9. Possible Choices for Re-structuring International Equity Internalize more of portfolio: it’s easier to control asset allocation. Split external by region, making it easier to allocate assets (take away global manager’s asset allocation decision.) Move all money externally - no experienced in- house money manager (except Diver, who’s retiring). No in-house company research. Any role for using international equity for diversification?