Lecture Note 1 Forecasting and Finance Introduction to Empirical Methods
. Lochstoer
UCLA Anderson School of Management
Winter 2022
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. Lochstoer UCLA Anderson School of Management ()
Winter 2022
Main actors in Önancial markets
Institutional investors
Retail investors
Banks (commercial and broker-dealer) Central banks (in U.S., the Federal Reserve)
. Lochstoer UCLA Anderson School of Management () Winter 2022
Common problem
Make decisions today based on expectations about the future.
How do you form expectations about the future? Historical data and events?
Gut feeling?
All of the above?
. Lochstoer UCLA Anderson School of Management ()
Winter 2022
Investors: the benchmark case
Mean-variance problem at each time t. Find (Nt 1) portfolio weights: min ωt0 Vt ωt s.t. ωt0 μt = return target (e.g., 7%)
V Var Rexcess!, t tt+1
μ E Rexcess. t tt+1
“Excess” means in excess of a reference return (e.g., 1-month T-bill rate)
The t in Vart and Et refers to a conditional variance (covariance) and expectation, respectively
I That is, as of time t, with the information available to you, what are your forward-looking expectations
I.e., need to forecast expected excess returns on Nt assets and the
(Nt + 1) Nt /2 elements in the covariance matrix (variance and correlations)
. Lochstoer UCLA Anderson School of Management () Winter 2022 4 / 16
Active mutual funds: A fundamentals-based manager
“Our investment professionals donít just sit behind their screens, they go out into the Öeld to get the answers needed for your investments. Theyíre constantly on the lookout, analyzing the markets and the companies within them.
Classic “stock-picking” talk. But, in the end they need to make decisions on portfolio weights
Solution to last slideís problem:
ω =constantV 1μ
Thus, in the end, they make a quantitative decision on a forecasting problem . Lochstoer UCLA Anderson School of Management () Winter 2022 5 / 16
Active mutual funds: A classic quant-based manager
“While weíre known as a pioneer in quantitative investing, we also have considerable expertise in areas that involve fundamental analysis or portfolio manager discretion. We use a combination of quantitative and qualitative tools to uncover independent, hard-to-Önd sources of return across global public and private markets.”
“Within the D. E. Shaw group, we run on collaboration, not internal competition. Teams work together to share trade ideas, identify and address risks, build tools, and explore new opportunities. Our sta§ includes world-class mathematicians, physicists, computer scientists, economists, analysts, business-builders, and system architects relying on specialized trading, operational, and compliance expertise developed over 30 years.”
. Lochstoer UCLA Anderson School of Management () Winter 2022 6 / 16
Benchmarking and the portfolio choice problem
Most managers have a benchmark index against which their investments are measured
This leads a minor modiÖcation of the portfolio choice problem. Instead of Rexcess = R R , we let Rexcess = R R
Thus, risk is meaured as “Tracking Error”:
TrackinpgError = σ (Rfund ,t Ridx ,t ) where σ () is short-hand for Var ()
Risk-reward ratio often expressed as an “Information Ratio”
InformationRatio =E(Rfund,t Ridx,t) σ(Rfund,t Ridx,t)
t t f,t t t idx,t
. Lochstoer UCLA Anderson School of Management ()
Winter 2022
Project (or Örm) valuations: capital budgeting
Classic NPV analysis:
Value = ∑∞ Et CFt+j t j
j =1 1 + DiscountRatet +j
Need to forecast current expecations of cash áows and the right discount rate
at each horizon j
This is also relevant for Private Equity and Venture Capital analysis, obviously
. Lochstoer UCLA Anderson School of Management () Winter 2022 8 / 16
Is lending or trading worth the cost of capital (often regulatory constraints)? Value of position = expected beneÖt from trade – cost of Önancing
For instance, deleveraging due to cost of leverage (market and/or regulatory) can force sales of assets which can drive leverage cycles
. Lochstoer UCLA Anderson School of Management () Winter 2022 9 / 16
Central Banks
The Fed has a joint employment, ináation, and Önancial stability goal Forecast expected future aggregate economic activity
Input to FOMC decision on whether to adjust interest rates or not Forecast e§ect of interest changes on economic activity (need model here)
Like standard NPV analysis, need to forecast distribution of outcomes not just one period ahead, but for multiple periods!
. Lochstoer UCLA Anderson School of Management () Winter 2022 10 / 16
This class
Forecasting
Multiple variables
Multiple horizons
Base material: standard quant time series analysis techniques Book for class
. Lochstoer UCLA Anderson School of Management ()
Winter 2022
Topic 1: today
Time series properties of stock market returns and prices
Class intro: Forecasting and Finance
The random walk hypothesis
Stationarity
Time-varying volatility and General Least Squares
Robust standard errors and OLS
. Lochstoer UCLA Anderson School of Management ()
Winter 2022
Topic 2: Time-dependence and predictability
ARMA models
The likelihood function, exact and conditional likelihood estimation
Predictive regressions, autocorrelation robust standard errors
The Campbell-Shiller decomposition
Present value restrictions
Multivariate analysis: Vector Autoregression (VAR) models, the
. Lochstoer UCLA Anderson School of Management () Winter 2022
Topic 3: Heteroskedasticity
Time-varying volatility in the data
Realized Variance
ARCH and GARCH models, application to Value-at-Risk
. Lochstoer UCLA Anderson School of Management () Winter 2022 14 / 16
Topic 4: The cross-section of stock returns
Single- and multifactor models
Economic factors: Models and data exploration
Statistical factors: Principal Components Analysis
Fama-MacBeth regressions and characteristics-based factors
. Lochstoer UCLA Anderson School of Management ()
Winter 2022
Class admin
60% Önal, 32% homeworks, 8% class participation
Class materials Textbook
Class notes posted on BruinLearn each week
Reference to textbook posted on BruinLearn each week
Use your pre-assigned groups
*Everyone* must have done homework even though you submit it as a group
I I discuss the homework each week *in class*, so having done it is an integral part of learning in the lectures
. Lochstoer UCLA Anderson School of Management () Winter 2022 16 / 16
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