Portfolio Management
Grenoble Ecole de Management
MSc Finance
2010
2
Learning Objectives
Mastering the principles of the portfolio
management process:
• Balanced portfolio
3
Balanced portfolio
• Equity portfolio + bond portfolio + derivatives + foreign
exchange positions + alternative = balanced portfolio
• How to mix different asset classes ?
4
Equity portfolio
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
5
Equity portfolio
Weights
Beta
Beta P
Sector A
6%
0,7
0,042
Sector B
4%
0,9
0,036
Country 1
8%
1,3
0,104
Country 2
4%
1,7
0,068
Country 3
12%
0,8
0,096
Small Cap
22%
1,6
0,352
Value stocks
24%
1,1
0,264
Index
20%
1
0,2
Total
100%
1,16
6
Equity + Bond portfolio
• 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.
7
Equity + Bond portfolio
Weights
Beta
Beta P
Sector A
6%
0,7
0,042
Sector B
4%
0,9
0,036
Country 1
8%
1,3
0,104
Country 2
4%
1,7
0,068
Country 3
12%
0,8
0,096
Small Cap
22%
1,6
0,352
Value stocks
24%
1,1
0,264
Index
20%
1
0,2
Total
100%
1,16
+
Weights
Sensitivity
Sensit P
Euro 2Y
50%
1,7
0,85
EURO 10Y
20%
7
1,4
Euro 30Y
5%
16
0,8
Cash
25%
0
0
Total
100%
3,05
8
50% Equity – 50% bonds portfolio
Weights
Beta
Beta P
Sector A
3%
0,7
0,021
Sector B
2%
0,9
0,018
Country 1
4%
1,3
0,052
Country 2
2%
1,7
0,034
Country 3
6%
0,8
0,048
Small Cap
11%
1,6
0,176
Value stocks
12%
1,1
0,132
Index
10%
1
0,1
Total
50%
0,58
Weights
Sensitivity
Sensit P
Euro 2Y
25%
1,7
0,425
EURO 10Y
10%
7
0,7
Euro 30Y
3%
16
0,4
Cash
13%
0
0
Total
50%
1,53
Beta balanced portfolio = 50%
beta equity portfolio
Sensitivity balanced portfolio =
50% sensitivity portfolio
9
Balanced portfolio
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.
Sector A
Sector B
Country 1
Country 2
Country 3
Small Cap
Value stocks
Index
Total
Euro 2Y
EURO 10Y
Euro 30Y
Cash
Total
Weights
3%
2%
4%
2%
6%
11%
12%
10%
50%
Weights
25%
10%
3%
13%
50%
Beta
0,7
0,9
1,3
1,7
0,8
1,6
1,1
1
Sensitivity
1,7
7
16
0
Beta P
0,021
0,018
0,052
0,034
0,048
0,176
0,132
0,1
0,58
Sensit P
0,425
0,7
0,4
0
1,53
Sector A
Sector B
Country 1
Country 2
Country 3
Small Cap
Value stocks
Index
Total
Euro 2Y
EURO 10Y
Euro 30Y
Cash
Total
Weights
29%
8%
1%
0%
14%
0%
4%
14%
70%
Weights
6%
9%
5%
10%
30%
Beta
0,7
0,9
1,3
1,7
0,8
1,6
1,1
1
Sensitivity
1,7
7
16
0
Beta P
0,203
0,072
0,013
0
0,112
0
0,044
0,14
0,58
Sensit P
0,102
0,63
0,8
0
1,53
However risk factors and curve risk are different between the portfolios.
10
New bond exposure
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.
0.9
0.8
0.7
0.6
0.5
Pfl 1
0.4
Pfl 2
0.3
0.2
0.1
0
Cash
Euro 2Y
EURO 10Y
Euro 30Y
11
Risk factors
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
12
Derivatives: Futures
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.
Sector A
Sector B
Country 1
Country 2
Country 3
Small Cap
Value stocks
Index ETF
Future Index
Total
Euro 2Y
EURO 10Y
Euro 30Y
Cash
Margin
Total
Weights
3%
2%
4%
2%
6%
11%
12%
10%
-15%
50%
Weights
25%
10%
2,5%
11,5%
1%
50%
Beta
0,7
0,9
1,3
1,7
0,8
1,6
1,1
1
1
Beta P
0,021
0,018
0,052
0,034
0,048
0,176
0,132
0,1
-0,15
0,43
Sensitivity
1,7
7
16
0
0
Sensit P
0,425
0,7
0,4
0
0
1,53
Hedge ratio = Beta Portfolio. Immunizing the
portfolio to equity risk requires a short position on
futures of 58%
13
Derivatives: Options
14
Derivatives: Options
Weights
Beta
Beta P
Sector A
3%
0,7
0,021
Sector B
2%
0,9
0,018
Country 1
4%
1,3
0,052
Country 2
2%
1,7
0,034
Country 3
6%
0,8
0,048
Small Cap
11%
1,6
0,176
Value stocks
12%
1,1
0,132
Index ETF
10%
1
0,1
Future Index
-15%
1
-0,15
Option Index
-2%
1
Total
50%
-0,02
0,41
Weights
Sensitivity
Sensit P
Euro 2Y
25%
1,7
0,425
EURO 10Y
10%
7
0,7
Euro 30Y
2,5%
16
0,4
Cash
11,5%
0
0
Margin
1%
0
0
Total
50%
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
Sector A
Sector B
Country 1
Country 2
Country 3
Small Cap
Value stocks
Index ETF
Future Index
Option Index
Total
Euro 2Y
EURO 10Y
Euro 30Y
Cash
Margin
Total
Weights
3%
2%
4%
2%
6%
11%
12%
10%
-15%
Beta
0,7
0,9
1,3
1,7
0,8
1,6
1,1
1
1
Beta P
0,021
0,018
0,052
0,034
0,048
0,176
0,132
0,1
-0,15
-4,3%
1
-0,043
0,39
50%
Weights
25%
10%
2,5%
11,5%
1%
50%
Sensitivity
1,7
7
16
0
0
Sensit P
0,425
0,7
0,4
0
0
1,53
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 0.0045%.
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.
Strong assumption: all other assets prices are unchanged
16
Foreign exchange position
Sector A
Sector B
Country 1
Country 2
Country 3
Small Cap
Value stocks
Index ETF
Future Index
Option Index
Total
Euro 2Y
EURO 10Y
Euro 30Y
Cash
Margin
3-month Fw 1,4
EUR IR
US IR
Total
Weights
3%
2%
4%
2%
6%
11%
12%
10%
-15%
-4,3%
50%
Weights
25%
10%
2,5%
11,5%
1%
Sensitivity
1,7
7
16
0
0
Sensit P
0,425
0,7
0,4
0
0
-3%
3%
0
0
0
0
50%
Beta
0,7
0,9
1,3
1,7
0,8
1,6
1,1
1
1
1
Beta P
0,021
0,018
0,052
0,034
0,048
0,176
0,132
0,1
-0,15
-0,043
0,39
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.
1,53
Profit = S – F ; Max[0,(S-F)] if optional ;
realized discount or premium will increase
the cash account
17
Alternative: Long – short position
Sector A
Sector B
Country 1
Country 2
Country 3
Small Cap
Value stocks
Index ETF
Future Index
Option Index
Total
Euro 2Y
EURO 10Y
Euro 30Y
Cash
Margin
3-month Fw 1,4
Beta
0,7
0,9
1,3
1,7
0,8
1,6
1,1
1
1
1
Beta P
0,021
0,018
0,052
0,034
0,048
0,176
0,132
0,1
-0,15
-0,043
50%
Weights
25%
10%
2,5%
10,5%
2%
Sensitivity
1,7
7
16
0
0
0,39
Sensit P
0,425
0,7
0,4
0
0
0
0
0
0
EUR IR
-3%
US IR
3%
Total
Overlay/alternative
L/S
Small Cap
Large Cap
Portable alpha
Fund HugeReturns
Future Index
Etc…
Total Equity
Weights
3%
2%
4%
2%
6%
11%
12%
10%
-15%
-4,3%
50%
1,53
20%
-20%
1,6
0,9
0,32
-0,18
10%
-10%
1,3
1
0,13
-0,1
50%
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.
18
Learning Objectives
Mastering the principles of the portfolio
management process:
• Portfolio insurance
Portfolio insurance aims at hedging portfolio from market downside risk.
19
Stop loss
• 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.
20
Constant Proportion Portfolio
Insurance
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:
21
Constant Proportion Portfolio
Insurance
With Wt 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 t0
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:
22
Constant Proportion Portfolio
Insurance: data manipulation
Initial portfolio value 10000, final floor 10949,
coefficient 3, tolerance 10%, risk free rate 4%
Years
Index price
Portfolio
Floor
Cushion
Exposure
Reserve
0
2000
10000
8000
2000
6000
4000
1
2200
10760
8320
2440
7320
3440
2
2000
10232
8653
1579
4738
5494
3
1800
9978
8999
979
2938
7041
4
1600
9933
9359
574
1723
8210
5
1400
10046
9733
313
939
9107
6
1200
10276
10123
154
462
9815
7
1000
10592
10527
65
194
10398
8
800
10969
10949
21
62
10907
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.
23
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.