Asset Management Lecture Four

Outline for today What assets to invest in a bear market? What assets to invest in a bear market? The BEARX Case The BEARX Case Index model Index model The optimal risky portfolio in the Single-factor index model The optimal risky portfolio in the Single-factor index model The information ratio The information ratio

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. 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 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 betting against the market by using derivatives such as stock index futures and options

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. Only the Prudent Bear fund (BEARX) has a positive 10-year return return. BEARX strategy: BEARX strategy: short-sale picks short-sale picks Whole Foods Market Whole Foods Market Starbucks Starbucks General Motors General Motors Buy into the precious-metals sector Buy into the precious-metals sector Gold Gold Miners such as Newmont Mining and AngloGold Ashanti Miners such as Newmont Mining and AngloGold Ashanti

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

Why gold? Why gold? Gold can serve as a “safe haven” Against inflation

The BEARX Case

Why gold? Why gold? Gold can serve as a “safe haven” Against inflation Against financial crisis

The BEARX Case

Why gold? 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

Threats to dollar stability: Threats to dollar stability:

The BEARX Case Threats to dollar stability: Threats to dollar stability:

The BEARX Case Why gold? 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

Why gold? 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

Comments on BEARX Comments on BEARX “Too One-Sided, Even in This Market” “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.” 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 N risky assets + the index portfolio Passive portfolio Active portfolio search for alpha efficient diversification

Optimal Risky Portfolio of the Single-Index Model

Maximize the Sharpe ratio Maximize the Sharpe ratio Expected return, SD, and Sharpe ratio: Expected return, SD, and Sharpe ratio:

Optimal Risky Portfolio of the Single-Index Model Weight of active portfolio position: Weight of active portfolio position:

Optimal Risky Portfolio of the Single-Index Model Modification of active portfolio position: Modification of active portfolio position: When When

The Information Ratio The Sharpe ratio of an optimally constructed risky portfolio will exceed that of the index portfolio (the passive strategy): The Sharpe ratio of an optimally constructed risky portfolio will exceed that of the index portfolio (the passive strategy): Information Ratio

The Information Ratio The optimal weight for each security is The optimal weight for each security is

Optimizing procedure

Table 8.2 Comparison of Portfolios from the Single-Index and Full-Covariance Models