Asset Management
Lecture Four
Outline for today
What assets to invest in a bear market?
 The BEARX Case
 Index model

The optimal risky portfolio in the Single-factor
index model
 The information ratio

What funds to invest
in a bear market?
What funds to invest
in a bear market?

Bear-market funds: designed to take
advantage of market downturns by making
investments whose value goes up when
stock prices decline.
selling stocks short -- picking companies
whose stock prices are expected to fall
 betting against the market by using
derivatives such as stock index futures and
options

What funds to invest
in a bear market?
What funds to invest
in a bear market?
What about 10 year return?
The BEARX Case


Only the Prudent Bear fund (BEARX) has a
positive 10-year return return.
BEARX strategy:

short-sale picks




Whole Foods Market
Starbucks
General Motors
Buy into the precious-metals sector


Gold
Miners such as Newmont Mining and AngloGold Ashanti
The BEARX Case
The BEARX Case
The BEARX Case
The BEARX Case
The BEARX Case
The BEARX Case

If you retired with $1 million with a 75%
equity allocation and a 5% withdrawal rate,
the value of the retirement portfolio after
20 years would be:
$ -180,727 if you retired in 1966
 $ -69,349 if you retired in 1972
 $3,575,760 if you retired in 1982

The BEARX Case
The BEARX Case
The BEARX Case
The BEARX Case

Why gold?

Gold can serve as a “safe haven”
 Against
inflation
The BEARX Case
The BEARX Case

Why gold?

Gold can serve as a “safe haven”
 Against
inflation
 Against financial crisis
The BEARX Case
The BEARX Case
The BEARX Case
The BEARX Case

Why gold?
Gold can serve as a “safe haven” against
inflation or financial crisis.
 Gold often trades inversely to the U.S. dollar,
making it a useful hedge in times of dollar
depreciation.

The BEARX Case
The BEARX Case

Threats to dollar stability:
The BEARX Case

Threats to dollar stability:
The BEARX Case

Why gold?
Gold can serve as a “safe haven” against
inflation or financial crisis.
 Gold often trades inversely to the U.S. dollar,
making it a useful hedge in times of dollar
depreciation.
 Gold can be viewed as an alternative asset
class.

The BEARX Case
The BEARX Case

Why gold?




Gold can serve as a “safe haven” against inflation or
financial crisis.
Gold often trades inversely to the U.S. dollar, making
it a useful hedge in times of dollar depreciation.
Gold can be viewed as an alternative asset class.
Gold, and even gold stocks, typically are not closely
correlated to either the stock or bond market.
The BEARX Case
The BEARX Case

Comments on BEARX
“Too One-Sided, Even in This Market”
 BEARX “offers a very reliable and predictable
course of action, so it's up to the investor to
decide WHEN to use his services and WHEN
NOT.”

Optimal Risky Portfolio
of the Single-Index Model

N risky assets + the index portfolio
Active portfolio
search for
alpha
Passive portfolio
efficient
diversification
Optimal Risky Portfolio
of the Single-Index Model
n 1
a p   wi ai
i 1
n 1
 p   wi  i
i 1
an 1  aM  0
 n 1   M  1
n 1
 (e p )   wi (ei )  (en 1 )   (eM )  0
2
2
i 1
2
2
Optimal Risky Portfolio
of the Single-Index Model

Maximize the Sharpe ratio
 Expected return, SD, and Sharpe ratio:
n 1
n 1
i 1
i 1
E ( RP )   P  E ( RM )  P   wi i  E ( RM ) wi i
 2  n 1

 n 1 2 2
 P       (eP )    M   wi  i    wi  (ei ) 
 i 1
  i 1

E ( RP )
SP 
2
P
P
2
M
2
1
2
2
1
2
Optimal Risky Portfolio
of the Single-Index Model
 Weight
of active portfolio position:
aA
when   1, wA0 
 A2
E ( RM )
 M2
Optimal Risky Portfolio
of the Single-Index Model
 Modification
of active portfolio position:
0
w
*
A
wA 
0
1  (1   A ) wA
 When
 A  1, w  w
*
A
0
A
The Information Ratio

The Sharpe ratio of an optimally constructed
risky portfolio will exceed that of the index
portfolio (the passive strategy):
 A 


s P s M  (eA ) 
2
2
Information
Ratio
2
The Information Ratio

The optimal weight for each security is
ai
2

(ei )
*
*
wi  wA n
ai

2

(ei )
i 1
2
 ai 
 aA 


  
i 1   (ei ) 
  (e A ) 
n
2
Optimizing procedure
ai
w  2
 (ei )
0
i
wi 
aA
2

(e A )
0
wA 
E ( RM )

 (eA )   wi2 2 (ei )
a A   wi ai
n
2
i 1
i 1
w
0
i
i 1
n
n
wi0
n
 A   wi  i
i 1
0
w
A
w*A 
1  (1   A ) wA0
wM*  1  w*A
2
M
E( Rp )  (wM*  w*A  A ) E( RM )  w*A A
 P  ( w  w  A )   w  eA 
*
M
*
A
2
2
M
*
A
2
Table 8.2 Comparison of Portfolios from
the Single-Index and Full-Covariance
Models