Portfolio Management Grenoble Ecole de Management MSc Finance 2010

Learning Objectives Mastering the principles of the portfolio management process: Balanced portfolio 2

3 Equity portfolio + bond portfolio + derivatives + foreign exchange positions + alternative = balanced portfolio How to mix different asset classes ?

Equity portfolio 4 Equity diversification relies on factor models: Sector allocation, geographic allocation Small cap versus large cap, low PE versus large PE Portfolio construction based on Beta calculations

Equity portfolio 5 WeightsBetaBeta P Sector A6%0,70,042 Sector B4%0,90,036 Country 18%1,30,104 Country 24%1,70,068 Country 312%0,80,096 Small Cap22%1,60,352 Value stocks24%1,10,264 Index20%10,2 Total100% 1,16

Equity + Bond portfolio 6 Bond portfolio risk cannot be measured with betas because maturities differ between bonds. They also change during all the life of one bond. Some securities may have embedded options, such has calls, puts, sinking fund provisions and prepayments. These features change the security characteristics over time and further limit the use of historical estimates. One has to use the concepts of duration, sensitivity and convexity to optimally build a bond portfolio.

Equity + Bond portfolio 7 WeightsSensitivitySensit P Euro 2Y50%1,70,85 EURO 10Y20%71,4 Euro 30Y5%160,8 Cash25%00 Total100% 3,05 WeightsBetaBeta P Sector A6%0,70,042 Sector B4%0,90,036 Country 18%1,30,104 Country 24%1,70,068 Country 312%0,80,096 Small Cap22%1,60,352 Value stocks24%1,10,264 Index20%10,2 Total100% 1,16 +

50% Equity – 50% bonds portfolio 8 WeightsBetaBeta P Sector A3%0,70,021 Sector B2%0,90,018 Country 14%1,30,052 Country 22%1,70,034 Country 36%0,80,048 Small Cap11%1,60,176 Value stocks12%1,10,132 Index10%10,1 Total50% 0,58 WeightsSensitivitySensit P Euro 2Y25%1,70,425 EURO 10Y10%70,7 Euro 30Y3%160,4 Cash13%00 Total50% 1,53 Beta balanced portfolio = 50% beta equity portfolio Sensitivity balanced portfolio = 50% sensitivity portfolio

Balanced portfolio 9 WeightsBetaBeta P Sector A29%0,70,203 Sector B8%0,90,072 Country 11%1,30,013 Country 20%1,70 Country 314%0,80,112 Small Cap0%1,60 Value stocks4%1,10,044 Index14%10,14 Total70% 0,58 WeightsSensitivitySensit P Euro 2Y6%1,70,102 EURO 10Y9%70,63 Euro 30Y5%160,8 Cash10%00 Total30% 1,53 WeightsBetaBeta P Sector A3%0,70,021 Sector B2%0,90,018 Country 14%1,30,052 Country 22%1,70,034 Country 36%0,80,048 Small Cap11%1,60,176 Value stocks12%1,10,132 Index10%10,1 Total50% 0,58 WeightsSensitivitySensit P Euro 2Y25%1,70,425 EURO 10Y10%70,7 Euro 30Y3%160,4 Cash13%00 Total50% 1,53 Weights are not useful to measure risk, use only betas and sensitivities. These two portfolios have different weights but exactly the same exposition to equity market and sensitivity risks. However risk factors and curve risk are different between the portfolios.

New bond exposure 10 Exposure to 2Y has decrease but to 30Y has increased. The fund is positioned for an over performance of the 30Y: flattening of the interest rate curve.

Risk factors 11 Yield curve changes include: a parallel shift in the yield curve change in the slope of the yield curve. a twist of the yield curve

Derivatives: Futures 12 When a transaction is initiated, the portfolio manager puts up a certain amount of money to meet the initial margin requirement. Both buyer and seller of futures contract must deposit margin. WeightsBetaBeta P Sector A3%0,70,021 Sector B2%0,90,018 Country 14%1,30,052 Country 22%1,70,034 Country 36%0,80,048 Small Cap11%1,60,176 Value stocks12%1,10,132 Index ETF10%10,1 Future Index-15%1-0,15 Total50% 0,43 WeightsSensitivitySensit P Euro 2Y25%1,70,425 EURO 10Y10%70,7 Euro 30Y2,5%160,4 Cash11,5%00 Margin1%00 Total50% 1,53 Hedge ratio = Beta Portfolio. Immunizing the portfolio to equity risk requires a short position on futures of 58%

Derivatives: Options 13

Derivatives: Options 14 WeightsBetaBeta P Sector A3%0,70,021 Sector B2%0,90,018 Country 14%1,30,052 Country 22%1,70,034 Country 36%0,80,048 Small Cap11%1,60,176 Value stocks12%1,10,132 Index ETF10%10,1 Future Index-15%1-0,15 Option Index-2%1-0,02 Total50% 0,41 WeightsSensitivitySensit P Euro 2Y25%1,70,425 EURO 10Y10%70,7 Euro 30Y2,5%160,4 Cash11,5%00 Margin1%00 Total50% 1,53 We buy put options to cover the market risk: Delta is 0.25 minimum quantity 10 the value of the index we cover is 5000 or 0.005% of the portfolio. Therefore the share of the portfolio we cover with one option is h = 0.005%*10*0.25 = 0.013%. Then to cover 2% of the portfolio we need to buy 160 put options.

15 Derivatives: Options Market performances deform the delta of the option. In this example the delta has a value of 0.6 for an index value of 4500 or %. Hedging reaches 4.3% of the portfolio. (160*0.0045%*10*0,6) Delta neutral policy would call for selling put options as to maintain the level of hedging unchanged. With 160 options I cover 4.3% of the portfolio. To cover 2% I need 74 options therefore I can sell 86 options. WeightsBetaBeta P Sector A3%0,70,021 Sector B2%0,90,018 Country 14%1,30,052 Country 22%1,70,034 Country 36%0,80,048 Small Cap11%1,60,176 Value stocks12%1,10,132 Index ETF10%10,1 Future Index-15%1-0,15 Option Index-4,3%1-0,043 Total50% 0,39 WeightsSensitivitySensit P Euro 2Y25%1,70,425 EURO 10Y10%70,7 Euro 30Y2,5%160,4 Cash11,5%00 Margin1%00 Total50% 1,53 Strong assumption: all other assets prices are unchanged

Foreign exchange position 16 WeightsBetaBeta P Sector A3%0,70,021 Sector B2%0,90,018 Country 14%1,30,052 Country 22%1,70,034 Country 36%0,80,048 Small Cap11%1,60,176 Value stocks12%1,10,132 Index ETF10%10,1 Future Index-15%1-0,15 Option Index-4,3%1-0,043 Total50% 0,39 WeightsSensitivitySensit P Euro 2Y25%1,70,425 EURO 10Y10%70,7 Euro 30Y2,5%160,4 Cash11,5%00 Margin1%00 3-month Fw 1,4 EUR IR-3% 00 US IR3% 00 Total50% 1,53 Foreign exchange position based on forward contract. Equivalent to borrowing in one currency and lending in the other one. No interest rate risk, risk might be measured by the beta. For a currency quoted directly (EUR/USD = 1.40): F=S(1+r*)/(1+r) With F and s respectively the direct quotation of the forward and spot of the domestic currency and r* and r the short term interest rate of the foreign and domestic currencies. Profit = S – F ; Max[0,(S-F)] if optional ; realized discount or premium will increase the cash account

Alternative: Long – short position 17 WeightsBetaBeta P Sector A3%0,70,021 Sector B2%0,90,018 Country 14%1,30,052 Country 22%1,70,034 Country 36%0,80,048 Small Cap11%1,60,176 Value stocks12%1,10,132 Index ETF10%10,1 Future Index-15%1-0,15 Option Index-4,3%1-0,043 Total50% 0,39 WeightsSensitivitySensit P Euro 2Y25%1,70,425 EURO 10Y10%70,7 Euro 30Y2,5%160,4 Cash10,5%00 Margin2%00 3-month Fw 1,4 EUR IR-3% 00 US IR3% 00 Total50% 1,53 Overlay/alternative L/S Small Cap20%1,60,32 Large Cap-20%0,9-0,18 Portable alpha Fund HugeReturns10%1,30,13 Future Index-10%1-0,1 Etc… Total Equity50% 0,56 Introduction of an arbitrage position or long-short position. Either risk neutral (zero-beta) or cash neutral strategies. Cash neutral arbitrage of small cap versus large cap in the example. Introduction of a portable alpha strategy: buy a fund and sell the market as to capture only the over performance of the fund (alpha) but not the market risk. This increase the position in future therefore the margin requirement increase. This might be cash consumer if the size of the fund cannot increase.

Learning Objectives Mastering the principles of the portfolio management process: Portfolio insurance 18 Portfolio insurance aims at hedging portfolio from market downside risk.

Stop loss 19 Stop loss: i) a maximum acceptable loss (which defines the floor of the value of the portfolio) is set at the beginning of the investment period ii) once this floor is reached, the fund is fully invested in the risk free rate to maturity. main limitation: if the drawdown happens at the beginning of the investment period you may gain only the risk-free rate missing the subsequent returns of the market. modified stop loss enables one to transfer only a portion of the NAV of the fund. This portion is related to the distance to maturity. The closer to maturity, the larger the portion invested in the risk free rate.

Constant Proportion Portfolio Insurance 20 CPPI is a dynamic trading strategy aiming at protecting a portfolio while taking profit of market returns. A predefined share of the value of the initial investment is guaranteed. This guarantee (the floor at maturity) is based on the investment in a zero-coupon bond. With L the floor at maturity (in t periods) and r the discount factor, the initial value of the floor is F:

Constant Proportion Portfolio Insurance 21 With W t the value of the fund at time t, we define the cushion C as the difference between the value of the fund and the floor at t 0 Then the exposure to risky markets, e, is defined using the cushion and a coefficient m. Initially the exposure is: At any point in time we define the exposure as:

Constant Proportion Portfolio Insurance: data manipulation 22 YearsIndex pricePortfolioFloorCushionExposureReserve Initial portfolio value 10000, final floor 10949, coefficient 3, tolerance 10%, risk free rate 4% The floor might be also revaluated as to protect superior interim value of the fund (at a rate of 4% in this example). This called ratchet management.

Summary Building a portfolio is a dynamic process based on risk analysis (Betas, duration, default…). Combining and rebalancing these assets in an optimal way is key (optimization). Looking at weights in a portfolio is useless, only risk and relative risks matter. There exist methodologies to insure portfolios against market risks. 23