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CFA level 2 (Quantitative methods (Time series (Autoregressive correlation…

- - - - Correlation reflects chance dataset
      - Calculation mixes each of two variables with the third
      - Dependent and independent variable relate not directly but through third variable
  - - - Linear relation exists between dependent
        and independent variables
      - Independent variables are not random. There is no exact linear relation between independent variables
        
        Multicollinearity
        [independent variables are highly correlated]
        
        regression coefficients are inaccurate and coefficient t-tests unreliable
        
        difficult to isolate impact of each independent variable on the dependent variable
      - Expected value of the error term,
        conditioned on independent variables, is 0
        
        Model specification errors
        
        Misspecified functional form
        (omitting important variables; variable may need to be transformed; poling data incorrectly)
        
        time-series misspecification (including lagged dependent variables in a independent variables in regressions when there is a serial correlation of errors; including an independent variable that is function of the dependent variable; measuring independent variables with error; nonstationarity)
      - Variance of the error term is same for
        all observations
        
        Heteroskedasticity problem
        (variance of error term is not constant)
        
        Unconditional
        (heteroskedasticity is not related to
        independent variables (does not
        affect statistical inference)
        
        Conditional: heteroskedasticity is correlated
        with independent variables (causes F-test for
        overall significance of the regression and t-test
        for the significance of each regression coefficient to
        become unreliable
      - Error term is uncorrelated across observations
        
        Serial correlation
        [regression errors are correlated across observations. Could be
        positive or negative and has same effect on statistical inference as conditional hetereskdasticity
      - Error term is normally distributed
  - - - Stationarity conditions
      - Total correlation
      - Partial correlation
    - - Quantitative
      - Qualitative
    - - AR with Rho = 1
      - Not weakly dependent
      - Random walk with a drift
        
        It is mean non-stationary
        (tends to increase/decrease with time)
        
        Deterministic process
        
        Mean non-stationary,
        but variance constant
        
        Xe=at+Et
        
        Stochastic process
        
        Both mean and variance non-stationary
        (function of time)
        
        Xt=a+(Xt-1) + Et
    - - Highly persistent values
        (if value if highly persistent, then it
        is not weakly dependent => no
        CLM, LLN applied)
      - Conditions for stationairty
        
        Expected value of error term
        is zer
        
        Variance of error term
        is zero for all observations
        
        Error term is uncorrelated
        across observations
      - Dickey-Fuller test for unit root
        
        Reject null if t-stat
        is less than Dickey-Fuller
        critical value
        
        Augumented DF tests
        
        AR with trend
        
        How to work out integration order
        
        DF test for Xt
        
        Reject null
        
        Zero order I(i) -
        stationary order
        
        Do not reject => I(k), k>0
        
        DF of delta (Xt)
        
        Reject null => Stationary => I(i)
        
        Do not reject
        
        DF (delta(delta(Xt)
    - - ARCH - Autoregressive
        conditional heteroskedasticity
        model
      - ARCHp model
        (ARCH depending on errors of multiple
        past periods
      - GARCH model
        (Similar to ARMA models, very unstable)
    - - Unit root test required to
        confirm that time series are stationary
        
        Neither has unit root => accept
        
        Only one has unit root => reject
        
        Both have unit roots
        
        (Engle-Garner) Dickey-Fuller test
        (confirm that error terms of both do
        not have unit root)
        
        Errors have unit root => not covariance
        stationary => not cointegrated time
        series => do not use
        
        Errors do not have unit root =>
        covariance stationary time series =>
        cointegrated => OK to use
      - Cointegrated time series are series where
        long-term relationship exists
        and they do not diverge w/o reason
        in long run
  - - - Measuring discrete risk
        
        Decisions trees
        (for sequential and discrete rirks)
        
        Scenario analysis
        (worst, expected, best case)
      - Measuring continuous risk
        
        Simulations
- - - - Terminology
        
        Offer = quoted sell price
        
        Accept offer = pay the offer
        
        Bid = quoted buy price
        
        Accept bid = hit the bid
        
        Offer always higher
      - Factors of bid-ask spread
        
        Bid-offer spread in the
        interbank market
        
        Currency pair
        
        Time of day
        
        Size of transactions
        
        Relationship between the dealer
        and the client
    - - Mark-to-market value of fwd contract
    - - Covered interest rate parity
        
        Forward premium/discount
        Fp/b - Sp/b = Sp/b*((ip-ib)/(1+ib))
        
        Domestic currency will trade at forward premium (Ff/d>Sf/d) only if foreign interest rate exceeds domestic (if>id)
        
        Nominal interest rate spreads equal the percentage forward premium (or discount)
        
        Forward rate
        Fp/b=Sp/b((1+ip)/(1+ib))
      - Uncovered interest rate parity
        
        Differential in foreign and domestic interest rates equal to expected growth rate of foreign currency
      - Forward rate parity
        
        Assuming that the uncovered interest rate parity holds, forward premium (discount) on a currency equals expected appreciation (depreciation) of the domestic currency), equals to diff between foreign (price) and domestic (base) currencies
        (Ff/d-Sf/d)/Sfd = %change in expected Sf/d = if-id
        
        If both covered and uncovered rate parity holds, forward rate is an unbiased forecast of the future spot rate
      - Purchasing Power Parity
        
        Absolute version
        
        broad price level of the foreign country (Pf) should equal the currency-adjusted broad price level in the domestic country (Pd)
        Pf = (Sf/d)(Pd)
        
        Relative version
        
        percentage change in the spot exchange rate (%ΔSf/d) is determined by the difference between the foreign and domestic inflation rates (πf – πd)
        %change Sf/d = (πf – πd)
        
        ex ante version of PPP
        
        Expected change in the spot exchange rate should equal the expected difference between domestic and foreign inflation rates
        
        Relationship stands on periods ~ > 6 years
      - International Fisher Effect
        
        Difference in nominal interest rates across countries is defined solely by difference in inflation rates, i.e. real interest rates are equal, assuming same currency risk
      - If all parities hold => no possibility to earn consistent return on FX trading
        
        if all the key international parity conditions held at all times, then the expected percentage change in the spot exchange rate would equal
        
        the forward premium or discount (expressed in percentage terms);
        
        the nominal yield spread between countries; and
        
        the difference between expected national inflation rates.
    - - Borrow in low yield, invest in high-yield currency
      - Performs well unless there is a high volatility. Results in sharp sell of currency during stress times and causes currency crisis
    - - Current account imbalances
        
        Flow Supply/Demand channel
        Current account deficit results currency depreciation over time. Long lags occur prior currency adjusts.
        
        Portfolio balance channel
        
        wealth shift from deficit to surplus nations
        
        Debt sustainability channel
      - Capital Flows
        
        Changes in fiscal and monetary policy affect capital flows which affect FX rates
    - - Mundell-Fleming model
        
        Dependence of capital flows in interest rates
        
        In country with low capital mobility, change in rates will impact trade flows rather than capital flows
      - Monetary model
      - Portfolio balance approach
  - - - Key institutions for growth
        
        Savings and interests
        
        Financial markets and intermediaries
        
        Political stability, rule of law, property rights
        
        Education and healthcare
        
        Tax and regulatory systems
        
        Free capital flows
      - Potential growth
        
        How fast economy can grow without increasing inflation
        
        Potential growth for equity markets:
        
        %change in stock market equals to %change in GDP plus %change in share of earning in GDP plus %change in P/E ratio
        
        Potential GDP for fixed income:
        
        closer actual GPD growth to potential (lower GDP slack) => higher interest rates (due to expected higher higher income and thus higher prices)
        
        higher potential GDP => higher credit quality of FI securities (as those are backed by income)
        
        Central banks' decisions on monetary policy are affected by output gap (actual vs potential)
        
        Impacts credit rating of sovereign debt
        
        Impacts government decision on fiscal policy which compares current valance of payments vs BP at potential growth rate
        
        Growth accounting equation (based on Cobb-Douglas production function)
        
        ΔY/Y = ΔA/A + αΔK/K + (1 – α)ΔL/L
        
        growth rate of output equals the rate of technological change plus α times the growth rate of capital plus (1 – α) times the growth rate of labor.
        
        a and 1-a are output elasticity and shares of income attributed to K (capital) and L (labor)
        
        Used to calculate potential growth
        
        alpha is taken as one minus factor share in GDP
        
        A = TFP - is a residual and considered as exogenous in classic model. Defined using misc time series models
        
        Labor productivity growth accounting equation.
        
        Models potential GDP as a function of the labor input and the productivity of the labor input. No need to calculated TFP or capital. But incorporates both in labor productivity which makes it complex to analyse
        
        Growth rate of potential GDP = long-term growth rate in labor force + long-term growth rate in labor productivity
        
        Cobb-Douglas Production function
        Y = AF(K,L), where
        Y - total output
        A - total factor productivity
        F(K,L) - function of capital and labor
        
        Capital deepening - increase of capital-to-labor ratio.
        
        Reflects rising investment in economy
        
        Will increase as long as growth rate of capital exceeds growth rate of labor
        
        At the point where the marginal product of capital equals its marginal cost, profit maximizing producers will stop adding capital (i.e., stop increasing the capital-to-labor ratio).
        
        Extended production function
        Y = AF(N,L,H,Kit,Knt,Kp)
        
        Raw materials: natural resources such as oil, lumber, and available land (N)
        
        Quantity of labor: the number of workers in the country (L)
        
        Population growth
        
        labor force participation
        
        net migration
        
        average hours worked
        
        Human capital: education and skill level of these workers (H)
        
        Information, computer, and telecommunications (ICT) capital: computer hardware, software, and communication equipment (KIT)
        
        Non-ICT capital: transport equipment, metal products and plant machinery other than computer hardware and communications equipment, and non-residential buildings and other structures (KNT)
        
        Public capital: infrastructure owned and provided by the government (KP)
        
        Technological knowledge: the production methods used to convert inputs into final products, reflected by total factor productivity (A)
        
        Allows to overcome diminishing marginal returns
        
        R&D spending 0.3-2.2% of GDP in 1990-2009 on average worldwide
        
        Measured as TFP. Captures technological & organizational improvements. Calculated as residual from labor & capital
      - Theories of growth
        
        Classic model
        
        Thomas Malthus, 1798
        
        Technological progress and land expansion, which increase labor productivity, translate into higher population growth. Diminishing marginal returns growth eventually forced to zero.
        
        Neo-classical model
        
        Robert Solow, 1950s
        
        Y = AF(K,L) = AK^αL^(1–α) (Cobb-Douglas)
        
        The objective of the neoclassical growth model is to determine the long-run growth rate of output per capita and relate it to (a) the savings/investment rate, (b) the rate of technological change, and (c) population growth.
        
        Steady State Rate of Growth
        
        Such growth when output-to-capital ratio is constant
        
        ∆Y/Y = (θ)/(1 – α) + n = Growth rate of TFP scaled by labor factor share + Growth rate in the labor force
        
        sy = [(theta/(1-a))+b+n]*k
        Steady state equilibrium occurs at the output-to-capital ratio where the savings and actual gross investment per worker generated in the economy (sy) are just sufficient to (1) provide capital for new workers entering the workforce at rate n, (2) replace plant and equipment wearing out at rate δ, and (3) deepen the physical capital stock at the rate [θ/(1 – α)] required to keep the marginal product of capital equal to the rental price of capital.
        
        Endogenous growth theory
        
        TFP is internal rather external factor and is calculated using time-series analysis
        
        Convergence of GDP per capita in developed and developing economies
        
        Absolute convergence - growth rates
        
        Conditional convergence - covergence of levels of GDP per capita
        
        Club convergence - only for those countries which implemented reforms
        
        Convergence trap - failure to implement institutional reforms