CFA Level II Study Session 4

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CFA Level II Study Session 4

• Instructor Prof. John Veitch
• Economics, USF
• Slides at
• www.usfca.edu/economics/veitch

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CFA Level II Study Session 4

• 1.A. Growth and Accumulation

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Growth Accounting

• Prodn function shows how inputs are used to
  produce output.
• Prodn function is written as Y AF(K, N).
• Y is total output, K is capital stock, N is
  labor, and A is the level of technology
• Analyze changes in total output by using the
  production function to determine what part of the
  change should be attributed to changes in
  capital, labor and technology
• Or in per capita terms

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Growth Accounting Calculations

• The growth accounting equations can be used to
  analyze contributions to growth in either total
  or per capita output.
• Example 1 Given the following DY/Y ___, DN/N
  0.02, DK/K 0.06, DA/A 0.0, q 0.4
• Example 2 Given the following DY/Y ___, DN/N
  0.02, DK/K 0.06, DA/A 0.02, q 0.4
• Example 3 Given the following DY/Y 0.075,
  DN/N 0.02, DK/K 0.06, DA/A ___, q 0.4

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Per capita Output Investment
Output
per Worker
y Y/L
f(k)
y
c
Consumption per Worker
sf(k)
i
Investment per Worker
kK/L
Capital per Worker
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Changes in Capital Stock

• Two forces act to change the ratio of capital per
  worker.
• Actual Investment increases Capital stock.
• i sy sf(k).
• Breakeven Investment Two forces reduce capital
  per worker ratio.
• Depreciation a certain of capital wears out
  annually
• d depn rate, so Depreciation d x k
• Labor Growth add fixed of new workers each
  year
• n popn rate, so Capital for new workers n x
  k
• Change in Capital stock per worker is
• Dk Actual Investment Breakeven Investment

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Steady State Capital Stock

• Steady State equilibrium occurs when no change to
  capital stock per worker.
• occurs when Dk 0 i.e when sf(k) (nd)k.
• Level of capital-labor ratio where this occurs
  k.
• Steady state equilibrium occurs automatically.
• If Actual k lt k
• Then sf(k) gt (nd)k and so Dk gt0.
• Result is that Actual k increases towards k.
• Move to steady state level of capital per worker.
• Similar result if Actual k gt k.

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Steady-State Equilibrium
yY/L i I/L
f(k)
y
(nd)k
(nd)k2
i2
i(nd)k
i1
(nd)k1
kK/L
k1
k2
k
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Increase in Savings Rate
Investment
and
Depreciation
(nd)k
s2 f(k)
1
s1 f(k)
2
k
k1
k2
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Changes in the Growth Model

• Consider the results of an increase in a nations
  saving rate on the steady state.
• increase in the savings rate shifts up the saving
  curve.
• investment gt depreciation so capital per worker
  rises.
• new steady state has higher k and output per
  capita.
• Other questions that could analyze in this way
  are
• Change in depreciation rate of capital, d.
• Change in population growth rate, n.
• Convergence from less-developed state, k lt k.
• Increase in technology, upward shift in prodn
  function.

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CFA Level II Study Session 4

• 1.B. Growth and Policy

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Endogenous Growth

• Explains source of continuing technological
  progress.
• Generally these models have prodn function with
  exhibit increasing returns to scale (IRS).
• Source of IRS are externalities in production,
  not completely captured by any individual firm
  but rather spillover to all firms.
• Research Development generates discoveries
  available to all firms. This is the theory behind
  the Silicon Valleys success.
• Endogenous growth means the private return to the
  individual firm is less than total social return
  from investing activity.
• Result is that private firms may under-invest in
  RD relative to the benefits derived by society
  as a whole.
• Often justifies government financing of basic
  research, which may have little or no private
  return but huge social returns.
• This argument often illustrated by how DARPA
  turned into is now the internet.

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Types of Convergence

• Absolute convergence
• implies that economies with equal rates of
  saving, population growth and the same access to
  technology should converge to the same level of
  output per capita.
• Conditional convergence
• implies that economies with different rates of
  saving or population growth but the same access
  to technology may converge to the different
  levels, but the same growth rate, of output per
  capita.
• Type of Multiple Choice Question
• If Country A has a higher savings rate than
  Country B, then in steady state equilibrium
  Country As output per capita relative to Country
  Bs will
• Have a higher level and growth rate.
• Have a lower level and lower growth rate.
• Have a higher level but same growth rate.
• Have the same level but higher growth rate.

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Policies for Growth

• Restore macroeconomic stability primarily
  reducing structural government budget deficit and
  putting in place tight money policies to control
  inflation.
• Liberalize prices allow markets to determine
  prices rather than government price controls.
• Privatize Government-owned firms allow firms to
  respond to market conditions.
• Liberalize foreign trade allow domestic
  consumers and firms access to world markets.
• Establish Social Safety Net put in place
  policies and institutions that react to offset
  the effects of economic fluctuations.
• Develop laws and institutions put in place laws
  and institutions that protect the property rights
  necessary for a market-based economic system
  (i.e. contract and bankruptcy laws).

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Miscellaneous Issues for Growth

• In the classical model, the popn growth rate is
  fixed.
• This is not true empirically. Population growth
  depends on per capita income over a wide range of
  income.
• Poor countries tend to have high population
  growth rates high infant mortality rates abut
  even higher birth rates. As income rises,
  population growth falls lower infant mortality
  rates but even lower birth rates.).
• Arguments that the limited availability of
  natural resources places limits on economic
  growth, ignore the effects of technological
  progress.
• Technological progress allows the more efficient
  use of inputs, thus producing more output using
  fewer resources.
• Similar argument used to show that natural
  resources are not necessary for economic growth.

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CFA Level II Study Session 4

• 4. Analyzing the Firms Environment

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Top-Down Models

• Theory Linking Macro Conditions to Industry Sales
• Industry_Salest a b GDP_Growtht errort
• Estimated Regression of Historical Relationship
• Industry_Salest1 a b
  GDP_Growtht1 10.80 0.75
  GDP_Growtht1
• Set Macro Growth Forecast, find Industry
  Forecast
• Industry_Salest1 10.80 0.75 (4.0)
  13.80
• Determine Industry Sales Forecast Projected
  Industry Sales
  Industry_Salest1 x Average Price0 x (1
  expected inflation)
• Determine Firm Sales Forecast Projected
  Firm Sales Projected
  Industry Sales x Projected Firm Market Share

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Product Cycle Model

• see Level II 1999 Exam, Question 18 Answers
• Stage 1 Product Development and Introduction
• Sales levels/growth low due to lack of consumer
  awareness. Specialized production and
  distribution limit entry to early developers.
• Stage 2 Product Expansion
• Consumer awareness increases. Rapid sales growth
  plus limited competition generates large profits
  for initial producers.
• Stage 3 Maturity
• High profits attract additional entrants as
  specialized skills become widespread. Sales
  expand but at slower rate. Increased competition
  lowers profits. Low wage, overseas competition
  may reduce margins further.
• Stage 4 Decline
• Consumer demand falls off as target markets
  become saturated. Industry may even experience
  declining sales some firms may exit as a result.

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CFA Level II Study Session 4

• CFA Level II, 1999 Exam
• Question 4, Industry Models

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• 4. Pat Johnson, CFA, is a stock analyst who
  follows the toy industry. Johnson has concluded
  that the two major macroeconomic factors
  influencing the toy industry's U.S. domestic
  nominal sales (in millions, SALESt) are
• the population (in millions) of children 3-14
  years old (CHILDt), and
• nominal per capita GDP in U.S. dollars (GDPt).
• Using monthly data, Johnson obtains the
  following regression results (t-values shown in
  parentheses)
• SALESt 62.10 87.50 CHILDt 0.1974 GDPt
• (2.49) (2.02)
  (3.03)
• Number of observations 30
• Unadjusted R2 0.9699
• F-statistic 112.64
• Multiple standard error 13.31
• Correlation between CHILD and GDP 0.25
  (t-value 0.75)

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• Ex 4-1 Critical Values for Student's
  t-Distribution
• Degrees of Area in Upper
  Tail
• Freedom 5 2.5
• 26 1.706 2.056
• n-(k1) 27 1.703 2.052
• 28 1.701 2.048
• 29 1.699 2.045
• 30 1.697 2.042
• 31 1.696 2.040
• 32 1.694 2.037
•  Ex 4-2 Critical Values for F-Distribution at 5
  Level of Significance
• Degrees of Freedom Degrees of Freedom
  (df) for the Numerator
• for the Denominator 1
  2 3
• 26 4.23 3.37 2.98
• 27 n-(k1) 4.21 3.35 2.96
• 28 4.20 3.34 2.95
• 29 4.18 3.33 2.93
• 30 4.17 3.32 2.92
• 31 4.16 3.31 2.91

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• A. Evaluate the goodness of fit of the regression
  equation.
• B. Given Exhibits 4-1 and 4-2 (on page 17),
  evaluate and interpret the following hypotheses
  at the 95 percent confidence level
• i. All estimated coefficients of the independent
  variables are simultaneously equal to zero.
• ii. Each individual estimated coefficient is
  equal to zero.
• C. i. Define multicollinearity, and
  determine whether it is likely that
  multicollinearity exists in Johnson's regression
  results.
• ii. Discuss the problems in multiple regression
  analysis when the homoskedasticity assumption is
  violated.
• D. Calculate, based on the regression equation,
• i. the forecasted "industry nominal sales volume"
  if nominal per capita GDP (GDPt) is expected to
  be 500 and the population of children 3-14 years
  old (CHILDt) is expected to be 100 million
• ii. the approximate 95 percent confidence
  interval for the predicted nominal sales. Show
  your calculations.

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• Evaluate the goodness of fit of the regression
  equation.
• Use R2 of total variation in Sales explained
  by estimated model.
• In time series look for R2 gt .8 (except CAPM
  where R2 .35)
• In cross-section look for R2 gt .3
• B. Given Exhibits 4-1 and 4-2 (on page 17),
  evaluate interpret the following hypotheses at
  the 95 confidence level
• All estimated coefficients of the independent
  variables are simultaneously equal to zero.
• Use F-statistic to test H0 b2 b3 0 (joint
  significance of variables)
• Compare F-statistic to Fk n-(k1) F2, 27
  3.35
• Reject H0 as F-statistic 112.64 gt 3.35.
• Coefs. are jointly signif. different from zero.
• Each individual estimated coefficient is equal to
  zero.
• Use t-statistic to test H0 bi 0 i 2, 3
  (signif. of individ. variable)
• Compare t-statistic to t n-(k1) t 27 2.052
  at 5 signif level
• For CHILD Cannot reject H0 at 5 as t-stat
  2.02 lt 2.052. Coef. on CHILD is sot significantly
  different from zero at 5 level.
• For GDP Reject H0 at 5 as t-stat 3.03 gt
  2.052. Coef. on GDP is significantly different
  from zero at 5 level.

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• i. Define multicollinearity, and determine
  whether it is likely that multicollinearity
  exists in Johnson's regression results.
• Multicollinearity when the independent variables
  are highly correlated.
• Likely that no multicollinearity exists.
• Correlation between the two variables is 0.25,
  (less than 0.70 not a problem).
• Correlation not statistically significantly
  different from zero given t-value of 0.75.
• Discuss the problems in multiple regression
  analysis when the homoskedasticity assumption is
  violated.
• Heteroskedasticity implies standard errors of
  regression coefficients incorrect (either too
  small or too large). If a standard error is
  understated (overstated), the t-value will be too
  large (too small).
• May cause independent variables to appear
  significant when they are not, or it may cause
  independent variables to appear insignificant
  when they actually are significant.

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• D. Calculate, based on the regression equation,
• the forecasted "industry nominal sales volume" if
  nominal per capita GDP (GDPt) is expected to be
  500 and the population of children 3-14 years
  old (CHILDt) is expected to be 100 million
• The forecast "industry nominal sales volume" is
  calculated as follows
• SALES (US millions) 62.10 87.5(100)
  0.1974(500) 8,910.80
• the approximate 95 percent confidence interval
  for the predicted nominal sales. Show your
  calculations.
• The interval is SALES estimate /- t(Sy.12),
• SALES estimate 62.10 87.5(100) 0.1974(500)
  8,910.80
• t is the critical t-value for a 2-tailed test,
  at 95 percent confidence interval, with 27 d.f.
  2.052
• Sy.12 is the multiple standard error 13.31
• Using these values, the confidence interval is
• 8,910.80 /- 2.052(13.3 1), or 8,883.49 ,
  8,938.11

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• Johnson's results are evaluated by the firm's
  chief economist, Susan Yost, CFA. Yost suggests
  that the results can be improved by removing the
  effects of inflation on SALESt, and GDPt.
• E. justify Yosts suggestion
• When inflation can influence both dependent and
  independent variables, the statistical results
  may be misleading. Both SALES and GDP should be
  inflation adjusted because may be a spurious
  correlation between nominal values.
• Removing inflation results in better model of
  true economic relation.
• In long run, consumer decisions are based on
  real values more than nominal values.
  Predictions based on real values may be more
  useful.
• In addition, in this regression, current GDP is a
  nominal variable but CHILD is not. By
  inflation-adjusting SALES and GDP, all of the
  variables in the equation become comparable.
• After the analyst has estimated constant dollar
  (real) sales, current dollar (nominal) sales may
  be obtained by adjusting predicted constant
  dollar sales by the expected inflation rate.
• Yost is justified in her comment.