Capital Asset Pricing Model

The capital asset pricing model (CAPM) is a theoretical framework predicts equilibrium expected returns on risky assets. CAPM is a one-factor model.


Here are the assumptions of the CAPM:

1. Individual behavior
a. Investors are rational, mean-variance optimizers.
b. Their common planning horizon is a single period.
c. Investors all use identical input lists, an assumption often termed homogeneous expectations. Homogeneous expectations are consistent with the assumption that all relevant information is publicly available.

2. Market structure
a. All assets are publicly held and trade on public exchanges.
b. Investors can borrow or lend at a common risk-free rate, and they can take short positions on traded securities.
c. No taxes.
d. No transaction costs.

The CAPM is based on two sets of assumptions, listed above. The first set pertains to investor behavior and allows us to assume that investors are alike in most important ways, specifically that they are all mean-variance optimizers with a common time horizon and a common set of information reflected in their use of an identical input list. The second set of assumptions pertains to the market setting, asserting that markets are well-functioning with few impediments to trading. Even a cursory consideration of these assumptions reveals that they are fairly strong, and one may justifiably wonder whether a theory derived from them will withstand empirical tests. Therefore, we will devote considerable attention later in the chapter to how the predictions of the model may change when one or more of these restrictive assumptions are relaxed.

Still, the simple version of the CAPM is a good place to start. While the appropriate quantification of risk and the prediction for the exact risk–return trade-off may differ across more sophisticated variants of the model, the central implication of the basic model, that risk premia will be proportional to exposure to systematic risk and independent of firm-specific risk, remains generally valid in its extensions. In part because of this commonality, the simple CAPM remains in wide use despite its empirical shortcomings.

Therefore, we begin by supposing that all investors optimize their portfolios á la Markowitz. That is, each investor uses an input list (expected returns and covariance matrix) to draw an efficient frontier employing all available risky assets and identifies an efficient risky portfolio, P, by drawing the tangent CAL (capital allocation line) to the frontier as in Figure 9.1, Panel A. As a result, each investor holds securities in the investable universe with weights arrived at by the Markowitz optimization process. Notice that this framework employs Assumptions 1(a) (investors are all mean-variance optimizers), 2(a) (all assets trade and therefore can be held in investors’ portfolios), and 2(b) (investors can borrow or lend at the risk-free rate and therefore can select portfolios from the capital allocation line of the tangency portfolio).

The CAPM asks what would happen if all investors shared an identical investable universe and used the same input list to draw their efficient frontiers. The use of a common input list obviously requires Assumption 1(c), but notice that it also relies on Assumption 1(b), that each investor is optimizing for a common investment horizon. It also implicitly assumes that investor choices will not be affected by differences in tax rates or trading costs that could affect net rates of return (Assumptions 2[c] and 2[d]).

Not surprisingly in light of these assumptions, investors would calculate identical efficient frontiers of risky assets. Facing the same risk-free rate (Assumption 2[b]), they would then draw an identical tangent CAL and naturally all would arrive at the same risky portfolio, P. All investors therefore would choose the same set of weights for each risky asset. What must be these weights?

A key insight of the CAPM is this: Because the market portfolio is the aggregation of all of these identical risky portfolios, it too will have the same weights. (Notice that this conclusion relies on Assumption 2[a] because it requires that all assets can be traded and included in investors’ portfolios.) Therefore, if all investors choose the same risky portfolio, it must be the market portfolio, that is, the value-weighted portfolio of all assets in the investable universe. We conclude that the capital allocation line based on each investor’s optimal risky portfolio will in fact also be the capital market line, as depicted in Figure 9.1, Panel B. This implication will allow us to say much about the risk–return trade-off.


Harry Markowitz laid down the foundation of modern portfolio management in 1952. The CAPM was published 12 years later in articles by William Sharpe, John Lintner, and Jan Mossin. The time for this gestation indicates that the leap from Markowitz’s portfolio selection model to the CAPM is not trivial.

Risks in CAMP

In the CAPM, total risk can be broken into two components: systematic risk and unsystematic risk. Systematic risk is the portion of risk that is related to the market and that cannot be diversified away. Unsystematic risk is non-market risk, risk that is idiosyncratic and that can be diversified away. Diversified investors can demand a risk premium for taking systematic risk, but not unsystematic risk.

In the CAPM, investors are only rewarded for taking systematic risk.

The Model

Required rate of return = risk-free rate + risk premium

The formula is:

required return = risk-free rate + beta * (expected market return – risk-free rate)

Corporate Income Tax

The final large non-operating item is the tax expense. This is often a large amount that affects profit substantially. Differences in tax rates can be an important driver of value. Generally, there are three types of tax rates:

The statutory tax rate, which is the tax rate applying to what is considered to be a company’s domestic tax base.

The effective tax rate, which is calculated as the reported tax amount on the income statement divided by the pre-tax income.

The cash tax rate, which is the tax actually paid (cash tax) divided by pre-tax income.

Differences between cash taxes and reported taxes typically result from timing differences between accounting and tax calculations and are reflected as a deferred tax asset or a deferred tax liability.

In forecasting tax expense and cash taxes, respectively, the effective tax rate and cash tax rate are key. A good understanding of their operational drivers and the financial structure of a company is useful in forecasting these tax rates.

Differences between the statutory tax rate and the effective tax rate can arise for many reasons. Tax credits, withholding tax on dividends, adjustments to previous years, and expenses not deductible for tax purposes are among the reasons for differences. Effective tax rates can differ when companies are active outside the country in which they are domiciled. The effective tax rate becomes a blend of the different tax rates of the countries in which the activities take place in relation to the profit generated in each country. If a company reports a high profit in a country with a high tax rate and a low profit in a country with a low tax rate, the effective tax rate will be the weighted average of the rates, and higher than the simple average tax rate of both countries. In some cases, companies have also been able to minimize their taxes by using special purposes entities. For example, some companies create specialized financing and holding companies to minimize the amount of taxable profit reported in high tax rate countries. Although such actions could reduce the effective tax rate substantially, they also create risks if, for example, tax laws change. In general, an effective tax rate that is consistently lower than statutory rates or the effective tax rates reported by competitors may warrant additional attention when forecasting future tax expenses. The notes on the financial statements should disclose other types of items, some of which could contribute to a temporarily high or low effective tax rate. The cash tax rate is used for forecasting cash flows and the effective tax rate is relevant for projecting earnings on the income statement. In developing an estimated tax rate for forecasts, analysts should adjust for any one-time events. If the income from equity method investees is a substantial part of pre-tax income and also a volatile component of it, the effective tax rate excluding this amount is likely to be a better estimate for the future tax costs for a company. The tax impact from income from participations is disclosed in the notes on the financial statements.

Often, a good starting point for estimating future tax expense is a tax rate based on normalized operating income, before the results from associates and special items. This normalized tax rate should be a good indication of the future tax expense, adjusted for special items, in an analyst’s earnings model.

By building a model, the effective tax amount can be found in the profit and loss projections and the cash tax amount on the cash flow statement.3 The reconciliation between the profit and loss tax amount and the cash flow tax figures should be the change in the deferred tax asset or liability. (Institute 128-129)

Source: Institute, CFA. 2018 CFA Program Level II Volume 4 Equity. CFA Institute, 07/2017. VitalBook file.

Return on Equity

Return on equity (ROE) measures the rate of return on the money invested by common stock owners and retained by the company thanks to previous profitable years. It demonstrates a company’s ability to generate profits from shareholders’ equity (also known as net assets or assets minus liabilities).

ROE shows how well a company uses investment funds to generate growth. Return on equity is useful for comparing the profitability of companies within a sector or industry.

Investors generally are interested in company’s that have high, increasing returns on equity.

Return on Equity = Net Income / Average Common Shareholder’s Equity

The Mundell–Fleming model

The Mundell–Fleming model describes how changes in monetary and fiscal policy within a country affect interest rates and economic activity, which in turn leads to changes in capital flows and trade and ultimately to changes in the exchange rate. The model focuses only on aggregate demand and assumes there is sufficient slack in the economy to allow increases in output without price level increases.

In this model, expansionary monetary policy affects growth, in part, by reducing interest rates and thereby increasing investment and consumption spending. Given flexible exchange rates and expansionary monetary policy, downward pressure on domestic interest rates will induce capital to flow to higher-yielding markets, putting downward pressure on the domestic currency. The more responsive capital flows are to interest rate differentials, the greater the depreciation of the currency.

Expansionary fiscal policy—either directly through increased spending or indirectly via lower taxes—typically exerts upward pressure on interest rates because larger budget deficits must be financed. With flexible exchange rates and mobile capital, the rising domestic interest rates will attract capital from lower-yielding markets, putting upward pressure on the domestic currency. If capital flows are highly sensitive to interest rate differentials, then the domestic currency will tend to appreciate substantially. If, however, capital flows are immobile and very insensitive to interest rate differentials, the policy-induced increase in aggregate demand will increase imports and worsen the trade balance, creating downward pressure on the currency with no offsetting capital inflows to provide support for the currency.

The specific mix of monetary and fiscal policies in a country can have a profound effect on its exchange rate. Consider first the case of high capital mobility. With floating exchange rates and high capital mobility, a domestic currency will appreciate given a restrictive domestic monetary policy and/or an expansionary fiscal policy. Similarly, a domestic currency will depreciate given an expansionary domestic monetary policy and/or a restrictive fiscal policy. In Exhibit 5, we show that the combination of a restrictive monetary policy and an expansionary fiscal policy is extremely bullish for a currency when capital mobility is high; likewise, the combination of an expansionary monetary policy and a restrictive fiscal policy is bearish for a currency. The effect on the currency of monetary and fiscal policies that are both expansionary or both restrictive is indeterminate under conditions of high capital mobility.

When capital mobility is low, the effects of monetary and fiscal policy on exchange rates will operate primarily through trade flows rather than capital flows. The combination of expansionary monetary and fiscal policy will be bearish for a currency. Earlier we said that expansionary fiscal policy will increase imports and hence the trade deficit, creating downward pressure on the currency. Layering on an expansive monetary policy will further boost spending and imports, worsening the trade balance and exacerbating the downward pressure on the currency.

The combination of restrictive monetary and fiscal policy will be bullish for a currency. This policy mix will tend to reduce imports, leading to an improvement in the trade balance.

The impact of expansionary monetary and restrictive fiscal policies (or restrictive monetary and expansionary fiscal policies) on aggregate demand and the trade balance, and hence on the exchange rate, is indeterminate under conditions of low capital mobility. Exhibit 6 summarizes these results.

Exhibit 5 is more relevant for the G–10 countries because capital mobility tends to be high in developed economies. Exhibit 6 is more relevant for emerging market economies that restrict capital movement.

A classic case in which a dramatic shift in the policy mix caused dramatic changes in exchange rates was that of Germany in 1990–1992. During that period, the German government pursued a highly expansionary fiscal policy to help facilitate German unification. At the same time, the Bundesbank pursued an extraordinarily restrictive monetary policy to combat the inflationary pressures associated with unification. The expansive fiscal/restrictive monetary policy mix drove German interest rates sharply higher, eventually causing the German currency to appreciate.

Balance of Payment

Balance of payments accounts keep track of a country’s payments to and receipts from foreigners. Any transaction resulting in a receipt from foreigners is entered in the balance of payments accounts as a credit. Any transaction resulting in a payment to foreigners is entered as a debit.

Three types of international transaction are recorded in the balance of payments:

1. Transactions that arise from the export or import of goods or services and therefore enter directly into the current account.

For example, when a French consumer imports American blue jeans, for example, the transaction enters the U.S. balance of payments accounts as a credit on the current account.

2. Transactions that arise from the purchase or sale of financial assets. An asset is any one of the forms in which wealth can be held, such as money, stocks, factories, or government debt. The financial account of the balance of payments records all international purchases or sales of financial assets.

For example, when an American company buys a French factory, the transaction enters the U.S. balance of payments as a debit in the financial account. It enters as a debit because the transaction requires a payment from the United States to foreigners. Correspondingly, a U.S. sale of assets to foreigners enters the U.S. financial account as a credit. The difference between a country’s purchases and sales of foreign assets is called its financial account balance, or its net financial flows.

3. Certain other activities resulting in transfers of wealth between countries are recorded in the capital account. These international asset movements—which are generally very small for the United States—differ from those recorded in the financial account. For the most part they result from nonmarket activities or represent the acquisition or disposal of nonproduced, nonfinancial, and possibly intangible assets (such as copyrights and trademarks).

For example, if the U.S. government forgives $1 billion in debt owed to it by the government of Pakistan, U.S. wealth declines by $1 billion and a $1 billion debit is recorded in the U.S. capital account.

You will find the complexities of the balance of payments accounts less confusing if you keep in mind the following simple rule of double-entry bookkeeping: Every international transaction automatically enters the balance of payments twice, once as a credit and once as a debit. This principle of balance of payments accounting holds true because every transaction has two sides: If you buy something from a foreigner, you must pay him in some way, and the foreigner must then somehow spend or store your payment.