Tools and Approaches
Different tools are useful over different time horizons.
Over sufficiently long horizons estimation techniques assume a central tendency.
Statistical Methods
Sample statistics are clear and understandable but prone to sampling error.
Shrinkage estimation takes a weighted average of two estimates to reduce forecast error.
Time series estimation forecasts based on lagged values of the variables being forecast. They may explain historical data well but are not structural.
Forecasting Fixed Income Returns
DCF
This is the only model precise enough to use for individual fixed-income securities. Also useful for Macro analysis.
Allows for scenario adjustment by changing inputs.
If the investment horizon is different from the bonds time to maturity the yield-to-maturity will not equal the expected return. YTM also fails to reflect reinvestment as a component of return.
If the investment horizon equals the Macauley duration of the bond the reinvestment and horizon effects will offset each other. Return will be close to the YTM. The remaining difference will be due to the yield curve and delays in rate changes.
Over horizons shorter than the MacDur the capital gain effect will outweigh the reinvestment effect and vice versa.
The timing of rate changes over the investment horizon will not affect the capital gain/loss of the bond but will affect reinvestment returns. When rate changes are anticipated this can be controlled by conducting a different DCF analysis for each subperiod.
Equilibrium Model
Allows for consistency in estimation across asset classes. Black-Litterman framework.
Emerging Market Bonds
Emerging market bonds are issued in local currencies as well as hard currencies (foreign, widely used currencies).
Emerging market debt is more vulnerable to economic, political, and legal risks. These risks can be categorized as:
- Ability to Pay
- Willingness to Pay
Emerging markets are highly heterogeneous so risks must be considered individually for each economy.
Forecasting Equity Returns
Differences in mean equity returns between developed countries from 1900-2017 were not statistically significant.
DCF Approach
The Gordon model estimates required equity return by discounting dividends. It is less noisy than historical returns as it is not influenced by changes in P/E and E/GDP.
The Grinold-Kroner model adjusts the Gordon model to account for share repurchases.
\[ E(R_e) \approx \frac{D}{P} + (\%\Delta E - \%\Delta S) + \%\Delta \frac{P}{E} \]
\(S\) is shares outstanding
Expected cash flow: \(\frac{D}{P} - \%\Delta S\)
Expected earnings growth: \(\%\Delta E\)
Expected repricing: \(\%\Delta \frac{P}{E}\)
The only very long-run assumptions that are consistent with economically plausible relationships are \(\%\Delta E = \text{Nominal GDP growth}\), \(\%\Delta S = 0\), and \(\%\Delta \frac{P}{E} = 0\).
Equilibrium Approach
CAPM2 can be extended to model equity returns across markets. The Singer and Terhaar approach extends CAPM by assuming all markets are fully integrated and each asset class and country is priced independently.
\[ RP_i = \phi {RP_i}^{G} + (1 - \phi){RP_i}^{S} \]
\(\phi\) is the degree of global integration
\(\beta\) is the asset’s \(\beta\) wrt to the global market portfolio
Emerging Market Equity Considerations
Country factors are generally more important than global industry effects.
Important to consider standards, regulatory environment, investor rights, political risks.
Forecasting Real Estate Returns
Real estate is relatively illiquid and has high transaction costs.
Historical returns are generally based on appraisals rather than transactions. Appraisals are not representative of the market volatility and correlations as they are essentially weighted averages of unobserved “true” returns.
Appraisal data will understate volatility and will spuriously imply a lagged correlation with market variables that actually have an instantaneous effect.
Real Estate Cycles
Demand for real estate is highly cyclical due to the inelasticity of supply.
Generally the cycle is driven by a boom-bust cycle in real estate demand. The global financial crisis was an exception as it was driven by capital markets (excess leverage rather than overbuilding).
Cap Rate Return Estimation
The capitalization rate can be used to derive the required return.
Using the Gordon model: \[ E(R_{re}) = Cap + NOI Growth \]
or, over finite horizons: \[ E(R_{re}) = Cap + NOI Growth - \%\Delta Cap \]
Cap rates are higher for riskier properties.
Equilibrium Model
Real estate can be incorporated into the Singer-Terhaar model. Requires controlling data for smoothing and illiquidity.
Public Real Estate
Delevered REIT returns and volatilities are similar to direct ownership. REIT returns are more closely correlated to equity returns. In the long run REIT returns are more closely correlated to direct real estate returns than equity returns.
Long Term Returns
Residential real estate account for 75% of the total value globally.
A 2017 study found residential real estate outperformed all other asset classes with higher return and lower volatility since 1870. Effect was reversed since 1980.
Equity returns are highly correlated across countries but residential real estate is not.
Forecasting Exchange Rates
Exchange rates are very difficult to forecast.
No single approach is sufficient. Exchange rate forecasting techniques are not mutually exclusive.
Trade Approach
Trade affects the exchange rate through:
- Flows
- Quasi-arbitrage of prices
- Competitiveness
With perfect capital mobility exchange rates will adjust to eliminate arbitrage opportunities.
Hot money are a concern to central banks as they impair monetary policy (see the Mundell-Fleming model). They also encourage firms fund long term investment with short term borrowing which can be disastrous when financing dries up. The bank can sell government securities to maintain target interest rates or intervene in the currency market. Capital controls might be imposed if other attempts are ineffective.
Strong economic growth will weaken a currency. Large, persistent current account deficits will also put downward pressure on the exchange rate.
Forecasting Volatility
Estimating a Variance-Covariance Matrix
Sample Statistics
Computing a sample variance for each asset can generate a VCV matrix but only for a smaller number of assets than observations. It is also vulnerable to large sampling errors.
The number of observations should be at least 10 times the number of assets for the VCV to be reliable. Even then it might not be cross-sectionally consistent.
Factor Models
Variance is determined by an asset specific component while covariance is determined by exposure to common factors.
The ith assets return is given by: \[ r_i = a_i + \sum_{k=1}^K \beta_{ik}F_k + \epsilon_i .\]
This technique has less estimation error and fewer required observations than sample statistics. Nevertheless it will almost certainly be misspecified. The output VCV matrix will be biased from the true VCV and does not converge as sample size increases.
Estimating the wrong thing with precision instead of the right thing with lots of noise.
Shrinkage Estimation
Combining estimates can mitigate the effect of estimation error.
ARCH Models
Asset returns exhibit volatility clustering. Traditional methods assume constant true volatility but autoregressive conditional heteroskedasticity (ARCH) models allow time-varying volatilities.
Generally estimates are constrained to a few assets.
Adjusting a Global Portfolio
A reasonable allocation to a global portfolio can be adjusted by considering country, sector, and asset class exposures to macro risks.
Things to consider include:
- Country growth rate changes
- Growth favors equities especially if due to productivity.
- Global integration changes
- Increased integration should reduce required return under Singer-Terhaar
- Business cycle estimation
- Best time to buy is as the market approaches a trough
- monetary and fiscal policies
- Especially relevant when there is a shift in targets
- current account balances
- Reallocate from rising CA deficits to those with rising surpluses