Answer to Question #66302 in Finance for Abdul
A cornerstone of modern portfolio theory, the capital asset pricing model attributes stock returns to the individual security's volatility, relative to the market and the volatility of the market itself. Investors have similar expectations concerning the risk/return relationship of risky assets, they can borrow and lend at the risk-free rate and transaction costs and taxes equal zero. The model could determine the portfolio on the efficient frontier that is the market portfolio. The CAPM formula reads as follows:
E(r)=Rf + β(Rm- Rf) where E(r) is the expected return; β is the volatility of the market and Rm is the return of the market.
The Arbitrage Pricing Theory (APT)
In contrast to the CAPM, which explains stock returns as resulting from two variables, APT is a multi-factor model, positing that stock returns are attributable to several factors, some of which are systematic, others industry specific and other still unique to a particular company. The formula is stated thus:
R=a0 + b1F1+ b2F2...+bnFn + e where R=the security\'s return; a0=the expected return; bn-the sensitivity of the security to factor Fn-factors affecting the security (GDP, inflation).
As with the CAPM, the factor-specific betas are found via a linear regression of historical security returns on the factor in question. Unlike the CAPM, the APT, however, does not itself reveal the identity of its priced factors - the number and nature of these factors is likely to change over time and between economies. As a result, this issue is essentially empirical in nature. Several a priori guidelines as to the characteristics required of potential factors are, however, suggested:
1. their impact on asset prices manifests in their unexpected movements
2. they should represent undiversifiable influences (these are, clearly, more likely to be macroeconomic rather than firm-specific in nature)
3. timely and accurate information on these variables is required
4. the relationship should be theoretically justifiable on economic grounds
Chen, Roll and Ross (1986) identified the following macro-economic factors as significant in explaining security returns:
• surprises in inflation;
• surprises in GNP as indicated by an industrial production index;
• surprises in investor confidence due to changes in default premium in corporate bonds;
• surprise shifts in the yield curve.
As a practical matter, indices or spot or futures market prices may be used in place of macro-economic factors, which are reported at low frequency (e.g. monthly) and often with significant estimation errors. Market indices are sometimes derived by means of factor analysis. More direct "indices" that might be used are:
• short-term interest rates;
• the difference in long-term and short-term interest rates;
• a diversified stock index such as the S&P 500 or NYSE Composite;
• oil prices
• gold or other precious metal prices
• Currency exchange rates
The linear factor model structure of the APT is used as the basis for many of the commercial risk systems employed by asset managers.
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