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Matas Romero Ausejo [email protected]

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GESTIN DE PORTAFOLIOS Y PLANIFICACIN DE INVERSIONESPD2

CAPITAL MARKET EXPECTATIONS

I. EXERCISE 1Suppose an analyst values stocks using discount rates based on projected risk-free rates ranges of 3% to 5%. The same

analyst uses risk-free rate projections of 4% to 6% to determine the allocation to fixed income. Discuss the likely effect on

the investors asset allocation.

It is likely that the investors asset allocation will be too heavily weighted towards equity, given that the discount rates usedto determine the equity allocation will be lower that the used for fixed income. This example illustrates that high-quality

forecasts using capital market expectations should be consistent. They also should be objectively formed, unbiased, well

supported, and have a minimum amount of forecast error.

II. EXERCISE 2It is now January 2007. An analyst would like to forecast U.S. equity returns. She is considering using either 15 years of

historical annual returns or 50 years of historical annual returns. Provide arguments for and against each selection of data

length.

15 years: If the analyst uses 15 years of historical data, then her sample may be excessively influenced by the time span

chosen. In this case, the U.S. equity returns for the past 15 years are likely quite high relative to probable future returns.Using 15 years of historical data would also not provide enough data points for statistical calculations is annual return are

used. A longer time span of data would increase the precision of population parameter estimates.

50 years: Using 50 years of data may also be problematic if there has been regime change. For example, changes in Federal

Reserve policy may render stock return data from 50 years ago irrelevant. Although data availability and asynchronous data

can sometimes be a problem when using long time spans of data, this is unlikely the case for historical U.S. equity data.

III. EXERCISE 3An analyst realizes that the variance for an exchange rate tends to persist over a period of time, where high volatility is

followed by more high volatility. What statistical tool would the analyst most likely use to forecast the variance of the

exchange rate?

The analyst would most likely forecast the variance using time series analysis. In time series analysis, forecasts are

generated using previous values of a variable and previous values of other variables. If an exchange rate exhibits volatility

clustering, then its variance will persist for periods of time and can be forecasted using a times series model.

JP Morgan Model

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The term measures the relationship, or rate of decay, between volatility in one period to the next.

IV. EXERCISE 4Suppose an analyst is valuing two markets, A and B. What is the equity risk premium for the two markets, their expectedreturns, and the covariance between them, given the following?

Sharpe ratio of the global portfolio 0.29

Standard deviation of the global portfolio 8.0%

Risk-free rate of return 4.5%

Degree of market integration for Market A 80%

Degree of market integration for Market B 65%

Standard deviation of Market A 18%

Standard deviation of Market B 26%

Correlation of Market A with global portfolio 0.87

Correlation of Market B with global portfolio 0.63

Estimated illiquidity premium for A 0.0%

Estimated illiquidity premium for B 2.4%

First, we calculate the equity risk premium for both markets assuming full integration. Note that for Market B, the illiquidity

risk premium is added in:

ERPA = 0.87 x (0.18) x 0.29 = 4.54%

ERPB = 0.63 x (0.26) x 0.29 + 0.024 = 7.15%

The equity risk premium for both markets assuming full segmentation is:

ERPA = (0.18) x 0.29 = 5.22%

ERPB = (0.26) x 0.29 + 0.024 = 9.94%

Weighting the integrated and segmented risk premiums by the degree of integration and segmentation in each market:

ERPA = (0.80 x 0.0454) + [(10.80) x 0.0522] = 4.68%

ERPB = (0.65 x 0.0715) + [(10.65) x 0.0994] = 8.13%

The expected return in each market is then:

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RA= 4.5% + 4.68% = 9.28%

RB= 4.5 + 8.13% = 12.63%

The betas in each market are:

i= i,Mi/i

A = (0.87) (18) / 8 = 1.96

B = (0.63) (26) / 8 = 2.05

The covariance is then:

covi,j = i j2

M

covA,B = (1.96) (2.05) (8.0)2 = 257.15

V.

EXERCISE 5Are there any attractive investments during deflationary periods?

Bonds actually perform well during periods of falling inflation or deflation, because interest rates are declining. This holds

true as long as credit risk does not increase. Equities do poorly in periods of declining inflation or deflation due to declining

economic growth and asset prices. Deflation also reduces the value of investments financed with debt, such as real estate,

because leverage magnifies losses. Deflation is negative for cash, because the return on cash declines to near zero.

VI. EXERCISE 6During an economic expansion, an analyst notices that the budget deficit has been declining. She concludes that the

governments fiscal policy has shifted to a more restrictive posture. Comment on her conclusion.

Her conclusion may not be warranted. In an economic expansion, the budget deficit will decline naturally, because tax

receipts increase and disbursements to the unemployed decrease. The changes she is observing may be independent of the

governments fiscal policy. Note that only government directed changes in fiscal policy influence the growth of the

economy. Changes in the deficit that occur naturally over the course of the business cycle are not stimulative or restrictive.

VII. EXERCISE 7Calculate the short-term interest rate target given the following information.

Neutral rate 5.00%

Inflation target 3.00%Expected inflation 6.00%

GDP long-term trend 3.00%

Expected GDP 5.00%

The Taylor rule can be formalized as follows:

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In this example, the higher than targeted growth rate and higher than targeted inflation rate argue for a targeted interest

rate of 7.5%. This rate hike is intended to slow down the economy and inflation.

VIII. EXERCISE 8A forecaster notes that the yield curve is steeply upwardly sloping. Comment on the likely monetary and fiscal policies in

effect and the future of the economy.

If the yield curve is steeply upwardly sloping, then it is likely that both fiscal and monetary policies are expansive. The

economy is likely to expand in the future.

IX. EXERCISE 9An analyst would like to project the long-term growth of the economy. Which of the following would you recommend he

focus on: changes in consumer spending or potential changes in tax policy due to a new government coming into office?

Although consumer spending is the largest component of GDP, it is fairly stable of the business cycle. The reason is that

consumers tend to spend a fairly constant amount of over time. Thus, it is likely that the analyst should focus on the

potential change in tax policy. This governmental structural policy has a potentially large impact on the long-run growth

rate of an economy.

X. EXERCISE 10An analyst is evaluating an emerging market for potential investment. She notices that the countrys current account deficit

has been growing. Is this a sign of increasing risk? Is so, explain why.

When exports are less than imports, a current account deficit results. This can be problematic, because the deficit must be

financed through external borrowing. If the emerging country becomes overlevered, they may not be able to pay back their

foreign debt. A financial crisis may ensue foreign investors quickly withdraw their capital. The financial crises are

accompanied by currency devaluations and declines in emerging market asset values.

XI. EXERCISE 11An analyst is evaluating two countries. Maldavia has a GDP of $60 billion and has an economy that is dominated by the

mining industry. Oceania has a GDP of $1.2 trillion and has an economy that sells a variety of items. He is predicting a global

economic slowdown. What country is at greater risk?

A global economic slowdown would affect smaller countries with undiversified economies more, because economic links

are more important for the types of countries. Larger countries with diverse economies are less affected by events in other

countries.

XII. EXERCISE 12An analyst believes that GDP is best forecast using a system of equations that can capture the fact that GDP is a function of

many variables, both current and lagged values. Which economic forecasting method is she most likely to use?

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Econometric analysis would be the best approach to use. It can model complexities of reality using both current and lagged

values. Ordinary least squares regression is most often used, but other statistical methods are also available.

XIII. EXERCISE 13At a conference, Larry Timmons states that the relationship between short-term interest rates and long-term bond yield is

not uniform. He also states that the relationship between a domestic currency value and interest rate is not uniform.Explain what Timmons is talking about.

The relationship between short-term interest rates and long-term yield is not uniform, because although bond yields

usually increase when short-term rates increase, this is not always the case. If short-term rates increase enough such that a

recession becomes more likely, the yields on bonds will fall as investors anticipate that the demand for loanable funds will

fall.

The relationship between a domestic currency value and interest rates is not uniform, because although the currency value

will increase as interest rates increase, this is not the case if interest rates increase high enough to slow down the economy.

In this case, foreign investors shy away from the country, because the country become a less attractive place to invest.

XIV. EXERCISE 14At the beginning of the fiscal year, Tel-Pal, Inc., stock sells for $75 per share. There are 2,000,000 shares outstanding. An

analyst predicts that the annual dividend to be paid in one year will be $3 per share. The expected inflation rate is 3.5%. The

firm plans to issue 40,000 new shares over the year. The price-to-earnings ratio is expected to stay the same, and nominal

earnings will increase by 6.8%. Based upon these figures, what is the expected return on a share of Tel -Pal, Inc., stock in the

next year?

The equation for expected return on Tel-Pal Inc using these inputs is:

The expected return is 8.8%. The expected dividend return is 4%, and the expected percent increase in the number of

shares is 2%. Expected inflation is 3.5%, which should be subtracted from the nominal earnings forecast to get the forecast

of real earnings growth.

XV. EXERCISE 15An analyst forecasts the historical covariance of the returns between Tel-Pal stock and Int-Pal stock to be 1,024. A newly

forecasted covariance matrix predicts the covariance will be 784. The analyst weights the historical covariance at 30% and

the forecast at 70%. Calculate the shrinkage estimate of the covariance.

The shrinkage estimate is simply the weighted average of the historical value and the forecasted value. The shrinkage

estimate is:

856 = 30% x 1,024 + 70% x 784

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XVI. EXERCISE 16List and explain three psychological traps that would encourage an analyst to place too much weight on past information

and less weight on new information.

A) Anchoring Trap: The analyst places too much weight on the first information received. Once having formed anopinion, the analyst will not want to deviate too far from the first opinion as new information arrives.

B) Status Quo Trap:The analyst will not want to deviate too far from the recent past.C) The Prudence Trap:The analyst will tend to ignore information that will lead to extreme forecasts.D) The Recallability Trap: The analyst lets past disasters and dramatic events and ignores newer information.XVII. EXERCISE 17

An analyst notices that the growth of the national inventory-to-sales ratio has slowed in recent years. Identify the

traditional interpretation of this in the formation of capital expectations. Explain a recent phenomenon that would give

another interpretation of this slowing growth, which may reduce the ratios significance.

A) Traditional Interpretation: A slowing in the growth of the inventory-to-sales ratio has traditionally indicatedincreased pessimism by the business community. They slow inventory growth in an anticipation of slower future

sales, which should lower the expected earnings and the returns of capital markets.

B) Another Interpretation: Increased technology and just-in-time inventory approaches have allowed business toreduce the amount of inventory they hold. Thus, a slowing inventory growth may be positive as firms find ways to

lower the amount of inventory they must hold for each level of sales. This would be positive for earnings, because

it would lower costs.

XVIII.EXERCISE 18The phase of the business cycle where we most likely expect to observe rising short-term interest rates and flat bond yields

is:

A) Late expansion: Both short-term and long term rates increasing.B) Initial recovery: Low or falling short-term rates, and bond yields have bottomed out.C) Early expansion: In this period of the business cycle, we expect to observe rising short-term interest rates and flat

or rising bond yields.

XIX. EXERCISE 19An investor is considering adding three new securities to his internationally focused fixed-income portfolio. The securities

under consideration are as follows:

1-year U.S. Treasury note (noncallable);

10-year BBB rated corporate bond (callable);

10-year mortgage-backed security (MBS) (government-backed collateral).

The investor will invest equally in all three securities being analyzed or will invest in none of them at this time. He will only

make the added investment provided that the expected spread/premium of the equally weighted investment is at least

0.5% (50 bps) over the 10-year Treasury bond. The investor has gathered the following information:

Real risk-free interest rate 1.2%

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Current inflation rate 2.2%

Spread of 10-year over 1-year Treasury note 1.0%

Long-term inflation expectation 2.6%

10-year MBS prepayment risk spread (over 10-year Treasuries)a 95 bps

10-year call risk spread 80 bps

10-year BBB credit-risk spread (over 10-year Treasuries) 90 bpsaThis spread implicitly includes a maturity premium in relation to the 1-year T-note as well as compensation for theprepayment risk.

Using only the information given, address the following problems using the risk premium approach:

A) Calculate the expected return that an equal-weighted investment in the three securities could provide.B) Calculate the expected total risk premium of the three securities, and determine the investors probable course of

action.

A) Answer:

Real risk-free rate(%)

+ Expected inflation(%)

+ Spreads orpremiums (%)

=

Expected annua

fixed-incomereturn (%)

1-year U.S. T-note 1.2 + 2.6 + 0 = 3.8

10-year corp. bond 1.2 + 2.6 + 1.0 + 0.8 + 0.9 = 6.5

10-year MBS 1.2 + 2.6 + 0.95 = 4.75

*We assign the 10-year corporate a 1% maturity premium based on the 10-yar over 1-year government spread.

Estimate of the expected return of an equal-weighted investment in the three securities: (3.8% + 6.5% + 4.75%) / 5.02%.

B) The average spread at issue is [0 + (1.0% + 0.8% + 0.9%) + 0.95%] / 3 = 1.22%. As 1.22% - 1% = 0.22% is less than0.5%, the investor will not make the investment.

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