IF Topic 6

• - make porfolio decisions on the basis of mean (expected return) and variance (returns are multiivariate normally distributed)
• - have identical views about risky assets' mean returns, variance of returns and correlations
• -can buy and sell assets in any quantity without affecting price (price taker) ad all assets are marketable (can be traded)
• -can borrow and lend at the rf rate without limit, and they can sell short any asset in any quantity
• -pay no taxes on returns and pay no transaction costs on trades
• -Perfect capital market (all info is correctly reflected in prices)

• Review on Demostic Asset Pricing Models:
• Capm
• APT (Fama - French)

• International Asset Pricing Modelts:
• World CaPM
• Capm under Market Segmentation
• Capm with exchange rate risk
• International Fama French two factor model
• empirical Results

in market equilibrium, investors are only rewared for bearing systematic risk - the type of risk can not be diversified away.

Idiosyncratic risk can be mitigated through appropriate diversification

But fundamental idea remains that there is no reason to expected reward just for bearing risk. Otherwise, you'd make a lot of money in Las Vegas => if there is return for risk, it should be special

E(ri) = rf + Bi (E(rm) - rf)

Bi= Cov (ri, rm) / variance m

• where E(ri) is the expected return on asset i
• rf is the risk free interest rate
• Bi is the sensitivity of asset i to market movement
• E(rm) - rf is the amrket risk premium. E(rm) is the expected return on the market portfolio
• An asset's covariance with the market portfolio is the relevant risk measure.

• a. find Bi by having S&P 500 as proxy. Disadvantages:
• - Includes only US stocks
• - The Theoretical market portfolio should include all types of risky assets from all around the world.

Anormalies: (Fama French 1993)

• Facts:
• -small firm stocks tend to have higher returns than big stocks
• -Firm with high book to market ratios have higer returns
• -average returns on common stocks are related to firm characteristics like size, earnings/prices, cash flow/price, book-to-market equity, past sales growth, long term past return, and short term past return

ratio used to find the value of a company by comparing the book value of a firm to its market value. Book value is calculated by looking at the firm's historical cost, or accounting value. Market value is determined in the stock market through its market capitalization. Formula: book/ market value

• 1. there are sufficient number of securities to diversify away idiosyncratic risk
• 2. Investors are risk averse
• 3. Inresters can borrow and lend at rf rate
• 4. There are no market frictions (transaction costs, taxes, or restrictions on short selling)
• 5. No arbitrage opportunities (the law of one price, no free lunch)

E(ri) = rf + Bi1 F1 = rf + Bim (E(rm) - rf)

Each beta term is based on the covariance of the security's returns with that factor (non diversifiable risks)

Fj = is the extra expected return required because of security's sensitivity to the jth factor (its market price)

E(ri) -rf = Bi1(rm-rf) + bi2(SMB)+bi3(HML)

• SMB = “small [market capitalization] minus
• big”

• "Size"
• This is the return of small stocks minus that of large stocks. When small
• stocks do well relative to large stocks this will be positive, and when they do
• worse than large stocks, this will be negative.

• HML = “high [book/price] minus
• low”

• "Value" This is the return of value stocks minus growth
• stocks, which can likewise be positive or negative.

Jegadeesh & Titman (1993) categorized stocks into 10 equal sized portfolio according to return over the preceding 6 monthes and measured return after the porfolio formation for various holding periods. Strategy was:

• Buy winners: stocks with the highest return oaver the preceding 6 months
• Sell losers: stocks with the lowest return over the preceding 6 months

Short term Momentum (return continuation): Over the first twelve months, portfolios formed on past winners realized cummulative returns that were 9.5percent greater than returns to the portfolio of losers

Long run Reversal: This winner over Loser pattern subsequently reversed itself, with the winners giving up more than half of their accumulated gain over losers during the next 16 months

• - All assumptions of the local CAPM still holds
• -All investors determine their demand for each asset by a mean variance optimization using their domestic currency as base currency

Plus:

• Markets are perfectly intergreated:
• Foreign investor can freely invest in local market
• Local investor can freely invest outside the local market

No premiums for currency risk:

Investors across the world have identical consumption baskets

Real Prices of consumption goods are identical in every country. In other words, PP always hold exactly.

E(ri)=rf+Bi(E(rw)-rf)

Where Bi = Cov (ri, rw)/variance w

where E(ri) is the expected return on asset i

rf is the risk-free interest rate

βi is the sensitivity of asset i to market movements

• E(rw) - rf is the market risk premium. E(rw) is the expected return on the world market portfolio. (in
• dollar terms)

An asset’s covariance with the world market portfolio is the relevant risk measure. the market portfolio includes all assets in the world weighted according to their market values. (ex. Morgan Stanley Capital World Index (MSCI) World Index)

If world markets are segmented, then impediments to the flow of capital prevent investors from taking advantage of relative mispricing between countries. In this case, the prices of similar securities will not be the same in all markets

Most developed markets are considered to be integreated. Segmentation tends to be more apparent with emerging markets

something that makes progress, movement, or achieving something difficult or impossible

because of various impendiments to capital mobility:

Psychological barriers: Unfamiliarity with international markets (language, and info sources) may cause investors to limit foreighn investment

Legal retrictions: Institutional investors may be prohibited by domestic regulation from investing internationally. Additionally, local government may impose retriction on foreign investment flowing into or out of the country

Transaction cost: Transaction costs are higher in international investing

Discriminationatory taxation: foreign investment may be taxed at a higer rate that locally generated investment

Political risks: local government actions can cause changes in the value of invested funds

Foreign currency risks: foreign investors bear the risk of changes in the local market value of invested funds, as well as the risk of changes in the exchange rate btw the local and investor's home currency

If country's stock market is intergrated with the rest of the world, then World CAPM holds

If capital markets are fully segmented, then investors can only invest domestically => local CAPM holds

If a country is going through process of interegation: combination of both holds (Bekaert and Harvey, 1995)

E(ri) = rf + w [(BiwE(rw-rf)] + (1-w) [BilE(rl-rf)]

w variables that proxy for the degree of integration, like size of trade sector and equity market capitalisation to GDP

stock prices for firms that cross list from segmented market are expected to rise and their subsequent expected returns should fall as an additional built-in risk premium compensating for these barriers dissipates

Empirical Results:

• -abnormal stock returns around interlisting are positive
• -abnormal returns around interlisting vary across stocks by home market in ways related to differences in degrees of market segmentation. that is, firms from emerging markets experience larger abnormal returns than firms from developed markets.

These barriers dissipates because:

Depositary Receipts is negotiable certificate issued by a depositary bank for a number of non - us security held by the depositary's custodian in the home market of the non-US company

Segmentation of markets due to investment barriers create an incentive for firms to adopt financial policies to reduce their negative effects. particularly useful for firms in emerging markets where direct and indirect barriers to capital flows can be most acute.

something that makes progress, movement, or achieving something difficult or impossible

International CAPM (ICAPM)

Deviatons from PPP can be a major source of currency risk

Additional risk premiums are linked to an asset's sensitivity to currency movements. The different currency exposures of individual securities would be reflected in different expected returns.

The expected return on an asset i is a sum of the risk free rate plus the market risk premium plus various currency risk premiums:

• E(ri)= rf + Biw*RPw+yi1*SRP1+....+ yik*SRPk
• => exact form
• E(Ri-rf)=BiE(Rw-rf)+y1iE(s1-rf+rf1*)+y2iE(s2-rf+rf2*)+....+ykiE(sk-rk+rfk*)
• (expected excess return=beta *market risk premium + gamma 1 * currency risk premium 1 + gamma 2 * currency risk premium 2+ect. )

• B: world market exposure of asset = cov(Ri, Rw)/var (Rw)
• y: are the currency exposures or sensitivities (from 1 to k) = Cov (Ri,s)/var(s)
• RPw is world market risk premium
• SRPk: are currency risk premiums (dollar per currency k)

Foreign Currency Risk Premium (SRP) is defined as the expected return on an investment minus the domestic currency risk free rate. it exists becuase of forward Premium Puzzle

E(s)-(rf-rf*)

Apparently, Uncovered Currency Risk Premium (SRP -> exchange rate appreciation)

E(St-S(t-1))/S(t-1)) = E(s) = rf- rf*

*: foreign curency

• to use this model, one needs to estimate two types of variables
• -the market and currency exposures on each asset
• -the risk premiums on the global market and on currencies

Could be estimated historically by regressing the company's stock returns on the world market portfolio returns and currency returns (depends on the currency structure of its exports, imports, investmenets and financing)

Value stocks have higer mean returns than growth stocks in 12 of 13 international markets

the difference in mean return is 7.60% per year.

So... we should have multifactor models which are world market portfolio and global HML (a risk factor for relative distress)

FF model: E(ri)-rf = Bi (E(rw) - rf) + hi E(WHML)

WHML: the diff between the returns on global value (high book to market: H) portfolios and global growth (low book to market L) portfolios

There are no benefits of extending the three factor model to an international context:

E(ri) - rf = Bi(E(rw)-rf) + wsiE(WSMB) + whiE(HML) + lsiE(LSMB) + lhiE(LHML)

Growth: Shares in a company whose earnings are expected to grow at an above-average rate relative to the market

Value Stock: A stock that tends to trade at a lower price relative to it's fundamentals (i.e. dividends, earnings, sales, etc.) and thus considered undervalued by a value investor. Common characteristics of such stocks include a high dividend yield, low price-to-book ratio and/or low price-to-earnings ratio.

Rouwenhorst (1998) examine momentum in 12 European Stock markets:

Past winners outperformed losers by more than one percent per month after correcting for risk

Momentum was strongest in smaller firms, although it was present in all size deciles

International Momentum Return (average across 12 European countries, 1980-1995) return continuation lasts for about one year, and then is partially reverse

Momentum by country: a winner versus loser pattern was present in each of the twelve European stock markets, even after controlling for a country risk, market risk, and firm size effect.

Dumas and Solnik (1995) and De Santis and Gerard (1998) estimate the conditional version of ICAPMs, and find strongly support a model that includes both market and foreingn exchange risk

Bekaert and Harvey (1995) support a partial integrated model with time varying market integration of emerging market.

Zhang (2006) concludes that the conditional ICAPM with exchange risk performs the best

Kc = [D/(D+E)]Kd(1-t) + [E/(E+D)] Ke


Kc= Weighted average cost of capital (WACC)

D= Amount of Debt

E= Amount of Equity

E+D= Total Value of the Firm

t= Corporate Tax Rate

Kd= Before-tax cost of debt capital

Ke = Cost of equity capital