Department of Economics School of Business, Economics and Law at University of Gothenburg Vasagatan 1, PO Box 640, SE 405 30, Göteborg, Sweden +46 37 786 0000, +46 31 786 1326 (fax) www.handels.gu.se infohandels.gu.se Bachelor Thesis 2011 (15 ECTS) Department of Economics Authors: Roderick Nilsson 881221 [email protected]Victor Rohlin 861110 [email protected]Tutor: Lars-Göran Larsson ([email protected]) Economics Spring 2011 Post Bretton Woods study of an alternative efficient portfolio using CAPM.
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Department of Economics School of Business, Economics and Law at University of Gothenburg Vasagatan 1, PO Box 640, SE 405 30, Göteborg, Sweden +46 37 786 0000, +46 31 786 1326 (fax) www.handels.gu.se infohandels.gu.se
Aim of thesis ........................................................................................................................................ 6
Limitations and demarcations of study ............................................................................................... 6
Literature Review .................................................................................................................................... 7
Capital Asset Pricing Model (CAPM) .................................................................................................... 7
Assumptions of CAPM ..................................................................................................................... 7
Criticisms and limitations to CAPM ................................................................................................. 7
Capital market line (CML) .................................................................................................................. 10
Data ....................................................................................................................................................... 11
Stock indices ...................................................................................................................................... 11
Dow Jones Industrial Average ....................................................................................................... 11
S&P 500 COMPOSITE - PRICE INDEX (U$) ...................................................................................... 11
Ultimately the CAPM model can provide a good benchmark if investors hold highly diversified
portfolios with mostly passive investments assuming that correlations between assets remain fixed.
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Therefore the selected time period is of utmost importance in order to create a reliable model.
Expected return In order to properly evaluate an asset the actual return has to be calculated. It is calculated by taking
the difference in price 2 consecutive periods and put it in relation to the former period, thus resulting
in the nominal return. Forecasting the expected return for an arbitrary period is calculated by the
average return of all return datasets for each asset. (Bodie, 2008)
Risk level & Beta-value In financial theory, the risk is the probability that the actual return will differ from the expected
return. It can be measured in various ways but the most common is by the standard deviation of an
asset, which is retrieved by taking the square root of the variance. The standard deviation shows not
only downside risk but also returns that exceed the expected return. (Bodie, 2008)
Beta depicts the relationship of the asset or portfolio with the market as a whole. It measures the
variance that cannot be removed by diversification, i.e. the systemic risk. (Hillier, Ross, Westerfield,
Jaffe, & Jordan, 2009)
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Financial ratios A key feature in measuring risk-return ratios is by measuring how much an extra unit of excess return
will cost in terms of added risk for that very asset. Two major ratios are used; The Sharpe
ratio measures risk by the standard deviation of the asset, the Treynor ratio uses the systematic risk,
the asset’s beta as the risk factor. (Bodie, 2008)
A larger ratio is preferable in both cases.
Jensen’s alpha
Alpha is a measured value of the excess return for a portfolio given risk exposure, asset correlation
and the risk free rate. Created by M. Jensen (1968) it is the main indicator of investor performance
compared to market.
Variance & Covariance Matrix (VCM) & Correlation Matrix Calculations of the VCM and the correlation matrix are done with Excel analysis toolkit and are used
to construct the portfolios. Variances, i.e. the inherent covariance of a single asset, appear along the
diagonal and covariances between different assets appear in the off-diagonal sections. (Bodie, 2008)
Minimum Variance Portfolio (MVP) The MVP achieves the greatest power of diversification. It is constructed by weighing all the
individual assets in order to attain the portfolio with the greatest return to lowest risk. The MVP will
according to theory and empirical evidence display a lower standard deviation - risk - than any of the
individual assets. Finding the individual weights is done by equaling all the assets in the minimum
variance portfolio to have the same covariance - thus, the same contribution to variance. Therefore
the asset with the smallest weight has the largest contribution per unit weight and should be
dropped first. (Bodie, 2008)
Optimal Risky Portfolio (ORP) ORP achieves the greatest return in relation to amount of risk taken. Thus a rational and risk-willing
investor would combine a set off assets in order to acquire higher return and benefit from the
diversification effect that lowers the portfolio risk level. Calculating the weighting of assets in a
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composite portfolio enables the construction of a portfolio efficient frontier, i.e. a linear relationship
between risk and return (see figure 1). (Bodie, 2008)
Capital market line (CML) CML is the line of an investment opportunity set that illustrates the risk-return combinations
available to investors when combining a market portfolio and a risk free asset. The slope of the CML
has the coefficient of the Sharpe ratio starting off at the risk free rate. All portfolios on CML
represent the highest possible Sharpe ratio thus maximizing return in terms of risk. (Bodie, 2008)
Figure 2: The Capital Market Line (CAPM)
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Data The data used in this study is collected from various sources depending on the nature of the
commodity. Included are four major commodities, gold, silver, oil and wheat, all whose price is
denominated in U.S. dollars. As well as three of the world’s most widely traded exchange rates, the
Japanese Yen, the Swiss Franc and the British Pound, all directly paired with the U.S. dollar. Also
included are the assumed risk free asset, the 3-month U.S. Treasury bill and the Dow Jones Industrial
Average. The selected benchmark is the S&P 500 due to its specification and linkage to high market
cap equities, the largest 500 companies - thus creating a suitable proxy for the overall market.
Selected data consists of monthly observations stretching 40 years from January 1971 to January
2011, with oil as an exception as oil data ranges from the end of December 1970 to the end of
December 2010, which is assumed to be equal the following period (end of Dec 70 ~ beginning Jan
71). 1971 being a suitable start off point due to the U.S. suspension and later discontinuation of the
Bretton Woods system where they no longer could guarantee the redeemability of a dollar into gold,
i.e. the dollar became a fiat currency. (IMF, 2011)
Stock indices
Dow Jones Industrial Average
The Dow Jones I. A. is one of the oldest market indices in U.S. starting as a 12-stock industrial average
and currently grown to a 30-stock average consisting mostly of manufacturers of industrial and
consumer goods but also companies in the entertainment and financial industry as well as companies
in the information technology business. At the present time it is not calculated as a standard average
but as a price-weighted average that also takes the effects of stock splits into consideration. It is the
highest quoted index in all media. (CME Group Index Services, LLC, 2011)
Data, monthly end prices due to limitations assumed to be same as following months start price, for
the period 1970-12-31 - 2010-12-31 was acquired from CME Group. (*CME Group Index Services,
LLC, 2011)
S&P 500 COMPOSITE - PRICE INDEX (U$)
The S&P 500 has its focus on large cap companies traded on NYSE or NASDAQ. Since 1957 it has
provided a free-float capitalization-weighted index containing 500 leading U.S. companies in principal
industries. It reflects approximately 75% of the U.S. equities market and is a leading barometer in the
market due to its wide range of companies and sectors, not only including value stocks but also
growth stocks. Due to the characteristics of the index it is the benchmark. (Standard & Poor's, 2011)
Data, monthly start prices for the period 1971-01-01 - 2011-01-01 was acquired from Reuters
through DataStream. (Thomson Reuters , 2011)
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Commodities
Gold Bullion LBM (U$ per Troy ounce)
Gold has historically been regarded as a monetary medium and also as a safe haven for investors
when times have been unstable due to economic or political uncertainty. It is a frequently traded
precious metal and is sometimes almost thought of as a currency because of how it behaves in the
market, i.e. as a safe storage of purchasing power. Since 1919 markets have used The London Gold
Fixing as a pricing medium to price gold products and derivatives. The price is set two times a day by
the five members of the London Gold Market Fixing LTD and is determined by speculation thru
supply and demand in the market. (The London Gold Market Fixing Ltd, 2011)
Data, monthly start prices for the period 1971-01-01 - 2011-01-01 was acquired from Reuters
through DataStream. (Thomson Reuters , 2011)
Silver Fix LBM (U$ per Troy ounce)
As gold, silver is and has been a major tradable precious metal for investors for a very long time. It
usually tracks the changes in gold price with high correlation. However, inherently it is more volatile
than gold, mostly because of lower liquidity in the market. Due to lack of physical demand for the
commodity, large investors and speculators are able to influence the price. The price of silver is
determined almost in the same way as gold. The difference is that only three members of The
London Silver Market Fixing LTD set the price, and only once every day. (The London Silver Market
Fixing Ltd, 2005)
Data, monthly start prices for the period 1971-01-01 - 2011-01-01 was acquired from Reuters
through DataStream. (Thomson Reuters , 2011)
Oil Spot Price: West Texas Intermediate (U$ per barrel)
Oil has been drilled and used for centuries but it was not until the oil boom in the late 19th century
that it earned the status it has today. Because of its easy transportability and high energy density it
quickly became one of the most important energy sources man has come across. It is often referred
to as the “black gold”. The three main crude oil benchmarks are West Texas Intermediate (WTI),
refined in the Midwest and Gulf Coast regions, it is predominantly used in the U.S. and is the
commodity underlying the oil’s futures price on the New York Mercantile Exchange. Brent blend
found in the North Sea and mainly used in Europe and the Dubai crude extracted from Dubai. (BBC,
2007)
Data, monthly start prices for the period 1971-01-01 - 2011-01-01 was acquired from the Federal
Reserve Bank of St. Louis. (WTI | Federal Reserve Bank of St. Louis, 2011)
Wheat U.S. Cash price at principal markets (U$ per bushel)
Wheat has become one of the most important crops largely because it is easy to grow on a large
scale and it is easy to store for long periods of time. The large demand for wheat has mainly come
from demand of flour globally, due to increased population, but lately the main drivers of wheat
prices are the increase in use of bio fuels and the increase of meat consumption in the developing
world, as it requires a lot of grain to produce 1 kilogram of meat. Wheat in the commodities market
is classified in many different classes, based on the quality of the grain.
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Data, monthly start prices for the period 1971-01-01 - 2011-01-01 was acquired from U.S.
Department of Agriculture. In order to create a fair price, a wheat basket was constructed to provide
an average price independent from quality and location in the U.S. This basket was created with
equal weighting from these types of wheat: (USDA, 2011)
No. 1 hard red
winter (ordinary
protein), Kansas
City, MO
No. 1 hard red
winter (13%
protein), Kansas
City, MO
No. 2 soft red
winter, Chicago,
IL
No. 2 soft red
winter, St. Louis,
MO
No. 2 soft red
winter, Toledo,
OH
No. 1 soft white,
Portland, OR
Foreign exchange rates As for the foreign exchange rates included in this thesis, the Japanese Yen, the Swiss Franc and the
British Pound Sterling, are denominated in U.S. dollars. The currencies included all have strong ties to
the current reserve currency U.S. dollar and are all considered global currencies. They also place
among the top traded currencies in the foreign exchange market.
Because neither the European Euro nor the German D-mark fulfilled the 40-year time period
requirement both currencies were omitted for the purpose of this study.
Foreign exchange rate JPY/USD
Japan has a major capital market and is a big trading partner to the U.S. Their currency, the Japanese
Yen, has for long functioned as the borrowing currency in carry trades between exchanges due to
Japan’s almost non-existing interest rates since the 90’s. The Japanese Yen is a global currency and a
highly traded one in the foreign exchange market. Data, monthly start prices for the period 1971-01-
01 - 2011-01-01 was acquired from the Federal Reserve Bank of St. Louis, priced as JPY/USD and was
hence inverted in order to provide the dollar value for a Japanese Yen. (JPY | Federal Reserve Bank
of St. Louis, 2011)
Foreign exchange rate CHF/USD
The Swiss Franc has similarly to gold played the role as a so-called safe haven currency for investors
when global financial unrest has been present. It is a small economy relative to the U.S. The Swiss
Franc is also considered a global currency and places highly among the top traded currencies in the
foreign exchange market. Data, monthly start prices for the period 1971-01-01 - 2011-01-01 was
acquired from the Federal Reserve Bank of St. Louis, priced as CHF/USD and was hence inverted in
order to provide the dollar value for a Swiss Franc. (CHF | Federal Reserve Bank of St. Louis, 2011)
Foreign exchange rate GBP/USD
The British Pound Sterling serves as a global currency as well and is also considered one of the top-
traded currencies on the foreign exchange market. It is a major currency with a large capital market
and Britain has always been a large trading partner to the U.S. Historically it has been and still is a
very important market for trading commodities, such as gold and silver. Data, monthly start prices
for the period 1971-01-01 - 2011-01-01 was acquired from the Federal Reserve Bank of St. Louis,
priced as GBP/USD and was hence inverted in order to provide the dollar value for a British Pound.
(GBP | Federal Reserve Bank of St. Louis, 2011)
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Interest rates
3 Month U.S. Treasury (risk free rate)
U.S. three-month Treasury bill priced at secondary market rate on yearly discount basis in percent. In
order to calculate monthly returns rates have been divided by twelve, providing a monthly return.
Further divided by a 100 in order to obtain nominal return in its decimal form. (UST 3M | Board of
Governors of the Federal Reserve System, 2011)
Results Below is a presentation of relevant information and statistics extrapolated from the selected data