IF topic 5
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Mean - variance model/ Dominance Principle. Investors prefer a higher expected return to lower returns and dislike risks.
In reality, investors hold a broad portfolio of many securities because they can reduce risk by spreading the funds invested across many securities (Markowitz)
the algebra of portfolio theory
- Expected return on a portfolio
- E[rP] = Sum of wi E[ri]
- Portfolio variance
- Var(rP) = sum i sumj wi wj covij
- where covij = correlationij deviationi deviation j
The correlation Coefficient is a measure of the extent that two variable move or vary together.
it ranges btw -1 to +1
Positive: a high value on one variable is likely to be associalted with a high value on the other
Negative correlation: a high value on a variable is likely to be associated with a low value on the other
No correlation: values of each are independent of other
How diversification reduces Risk
Combining stocks into a portfolio reduces the variability of possible returns as long as the returns on the individual stocks are not perfectly corrected, ie. as long as their correlation coefficients are less than +1.00
If there are two components:
Variance: sP2 = wA2 sA2 + wJ2 sJ2 + 2 wA wJ rAJ sA sJ
How to form porfolio
we can vary:
- the number of assets that make up the portfolio
- the identity of the assets in the portfolio
- the weights assiged to each asset
Harry Markowitz's findings
theory of portfolio choice (1990)
- A porfolio is an efficient profolio if
- => no other portfolio with the same expected return has lower risk
- => no other portfolio with the same risk has a higer expected risk
Investor prefer efficient porfolios over inefficient ones. The collection of efficient portfolio is called an efficient frontier
Markowitz Efficient Frontier
Tobin's Separation Theorem
- All investors prefer a combination of
- 1. risk free asset
- 2. the market portfolio (consists of all risky assets and portfolios, each asset weight is proportional to its market value)
Such combination dominate all other assets and portfolio:
the returns will depend on return in the foreign market and change in exchange rate btw 2 currencies
Dolla value of an asset
- The dollar value of an asset is equal to its local currency value (V) multiplied by the exchange rate (S)
- (number of dollars/local currency):
V$ = V + S^($/f)
The rate of return over the period is
r$ = r f + s$/f + (r f * s$/f)
where r f = return in local currency
s = percentage exchange rate movement
E[r$ ] = E[r f]+E[s$/f]+E[r f x s $/f]
=Var(rf)+Var(s$/f)+Var(rfs$/f) 2Cov(rf,s$/f)+2Cov(rf, rf * s$/f)+2Cov(s$/f, rf*s$/f)
= Var(rf) + Var(s$/f) + (interaction terms)
low international correlation allows for reduction of volatility of a global portfolio and bigger risk reduction
International correlation and Structure and risk diversification
Security returns are much less correlated across countries than within a country (industry and country factos both seem important)
- - different industrial compositions and different industrial structures
- - they are imperfectly correlated across countries
- - Part of the benefit should therefore come from industrial diversification.
Differences in institutional and legal frameworks, technological specialization, independent fiscal and monetary policies, and cultural and sociological differences all contribute to the degree of a capital market's independence => business cycles are often high asynchronous across countries.
However, level of intergration increase => international correlation increases in periods of high market volatility espically in berar market but not in bull markets (Longin and Solnik, 2001) => correlation break down (benefits of international risk diversification disappear when they are most needed)
How to diversify internationally?
Incovenient way: purchase shares directly in foreign markets using foreign currencies
Exchange traded funds (ETFs):
- US Based International Mutual Funds
- Coutry funds: invests exclusively in the stocks of a single country
Investors can trade a whole stock market indix as if it were a single stock (ex. France, Germany, china, ..)
Hedge Funds: For example, J.P. Morgan provided access to the Jayhawk China Fund, a hedge fund investing in chineses stocks not readily available in U.S Markets
Home bias Puzzle (stock)
Refers to the extent to which portfolio investments are concentrated in domestic equities.
e.g: Sweden has 0.8% share in World market Value and 100% doestic equities in the portfolio
u.s has 36.4% and 98% domestic equities
Bull Market vs Bear Market
A financial market of a group of securities in which prices are rising or are expected to rise. The term "bull market" is most often used to refer to the stock market, but can be applied to anything that is traded, such as bonds, currencies and commodities.
A market condition in which the prices of securities are falling, and widespread pessimism causes the negative sentiment to be self-sustaining. As investors anticipate losses in a bear market and selling continues, pessimism only grows. Although figures can vary, for many, a downturn of 20% or more in multiple broad market indexes, such as the Dow Jones Industrial Average (DJIA) or Standard & Poor's 500 Index (S&P 500), over at least a two-month period, is considered an entry into a bear market.
Barriers to International Investment
Familiarity with Foreign Market:
cultrual differences, trading procedures, way reports are presentated, differetn languages, different time zones
some countries run the risk of being policically unstable in the form of polical, economic, or monetary crises
- liquidity issue: some markets are very small and others have many assets traded in large volumes
- Price manipulation and insider trading
can be hedgeed with derivatives, leads to additional administrative and trading cost
contraint the amound of foreign investmenet that can be undertaken by local investors/foreign investors are no allowed to become controlling shareholder. BUT restrictions on capital flows have fallen over times
Higer tax in foreign equity income. Double taxation on dividend and interest income distributions.
- Brokerage commissions (fixed, negotiable, variable schedule, part of bid -ask spread)
- The cost of trading is lower in liquid market such as NY
- transaction costs shold lead all investor toward the most liquid markets, no necessarily the domestic market
Strong and Xu (2003)
use Merrill Lynch survy of fund manager (US, UK, Japna, and Continental EU) => more optimistic about the domestic equity market
Investing in emerginng market
- - low correlation with developed country returns, high average returns, high volatility,
- -negative skewness (chance of an unexpected large negative movement in returns, more extreme negative returns than positive returns) =>Investment risk in emerging economies often comes from the possibility of financial creises (Mexican Peso crisis 1994, Asian financial crisis 1997 => contagion: currency is more likely to devalue if a neighboring country has experienced a devaluation) => mean variance might not be a good way of getting optimal portfolio choice
- - poor credit ratings and lack of high quality regulatory and accounting framwork
- -a poorly developed and supervised baking sector
- -short selling constraint
- -restrictions can take the form of foreign ownership,, repatriation of income or capital, discriminatory taxes, foreign currency restrictions, authorized investors
- -Corruption, poor corporate governace.
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