The Oxford Guide to Financial Modeling by Ho & Lee Chapter 1. Introduction: Discounted Cash Flow Method The Oxford Guide to Financial Modeling Thomas S. Y. Ho and Sang Bin Lee And material from: Holden, Peel, and Thompson text Copyright © 2004 by Thomas Ho and Sang Bin Lee. All rights reserved.

The Oxford Guide to Financial Modeling by Ho & Lee Chapter 1. Introduction: Discounted Cash Flow Method Examples of Financial Issues Investments Risk Management Corporate Finance How are these issues be related to each other? What are the financial decisions? What are the financial tools?

The Oxford Guide to Financial Modeling by Ho & Lee Chapter 1. Introduction: Discounted Cash Flow Method Financial Models Normative models –Subjective optimal solutions, objective functions Positive models –Equilibrium solutions Continuous time vs. Discrete time models –Technical constructs of modeling

The Oxford Guide to Financial Modeling by Ho & Lee Chapter 1. Introduction: Discounted Cash Flow Method 4 Financial Model Cycle

The Oxford Guide to Financial Modeling by Ho & Lee Chapter 1. Introduction: Discounted Cash Flow Method 5 Present Value Calculations Specification of the cash flows The time value of money and the discount rate

The Oxford Guide to Financial Modeling by Ho & Lee Chapter 1. Introduction: Discounted Cash Flow Method 6 Measures of Risk Utility function –Increasing utility of wealth –Decreasing marginal utility of wealth Risk aversion

The Oxford Guide to Financial Modeling by Ho & Lee Chapter 1. Introduction: Discounted Cash Flow Method 7 Concave Utility Function W WGWG W+G W U(W+G) U(W  G) U(W) 1/2[U(W+G)+U(W  G)]

The Oxford Guide to Financial Modeling by Ho & Lee Chapter 1. Introduction: Discounted Cash Flow Method 8 A risk-return relationship for risk-averse investors and risk-loving investors A A B B Investor is better off Risk Averse Investor Risk Loving Investor

The Oxford Guide to Financial Modeling by Ho & Lee Chapter 1. Introduction: Discounted Cash Flow Method 9 Discounted Cash Flow Method (DCF) Single payment –A zero coupon bond: present value discount factor Annuity payments –Equal payments over a period of time Perpetual payments –Equal payments forever Uneven cash flows –An stream of payments

The Oxford Guide to Financial Modeling by Ho & Lee Chapter 1. Introduction: Discounted Cash Flow Method 10 DCF Model

The Oxford Guide to Financial Modeling by Ho & Lee Chapter 1. Introduction: Discounted Cash Flow Method 11 Descriptions of the DCF Model The discount rate: The risk premium: The expected cash flows: CF The present value is the value of the future cash flows, which may be uncertain

The Oxford Guide to Financial Modeling by Ho & Lee Chapter 1. Introduction: Discounted Cash Flow Method 12 Holden, Peel, Thompson text Models are need to make forecasts which are essential for informed decision- making. Differences in Short- vs. Long-Term forecasts (and affects choice of model). Need to evaluate the effectiveness of forecasts. Common Benchmark: compare to a No- Change Forecast.

The Oxford Guide to Financial Modeling by Ho & Lee Chapter 1. Introduction: Discounted Cash Flow Method 13 Holden et al. text (cont.) Non-Causal vs. Causal Models Non-Causal examples: No-Change, Random Walk, and time series-based models such as ARIMA. Causal examples: fundamental-based models such as DCF, CAPM, Macroeconomic.

The Oxford Guide to Financial Modeling by Ho & Lee Chapter 1. Introduction: Discounted Cash Flow Method 14 Holden et al. text (cont.) Trend models: Y t = f(time) + u t No-Change / Random Walk: Y t = Y t-1 + u t ARMA: Y t = f(Y t-1, Y t-2, … Y t-N ) + u t Vector Autoregression (VAR): Y t = f(Y t-1, Y t-2, … Y t-N, X t-1, … X t-N ) + u t Causal / Fundamental: Y t = f(X t, Z t, …) + u t

The Oxford Guide to Financial Modeling by Ho & Lee Chapter 1. Introduction: Discounted Cash Flow Method 15 Holden et al. text (cont.) Statistical Measures of a Model’s Suitability: Adjusted R-square Parameter t-statistics (t-stat > |2.0| ?) Parameter signs consistent with theory. Variance Inflation Factors to test Multicollinearity Durbin-Watson statistic (between 1.6 – 2.4) Autocorrelation coefficients (close to zero?) No heteroskedasticity (past volatility is a factor? Check via White, LM, or other tests)

The Oxford Guide to Financial Modeling by Ho & Lee Chapter 1. Introduction: Discounted Cash Flow Method 16 Holden et al. text (cont.) Key Steps in Financial Modeling: 1.Select the correct / relevant theory. 2.Choose the proper equation(s) so that the model truly corresponds to the theory. 3.Collect data that accurately reflects the variables in your chosen model. 4.Estimate the parameters of your model using the correct statistical technique (e.g., OLS, MLE, simulation, etc.). 5.Evaluate the statistical significance of your model’s parameters. 6.Develop out-of-sample forecasts for the relevant time horizon. 7.Evaluate the accuracy of your model’s forecasts and revise model (as needed).

The Oxford Guide to Financial Modeling by Ho & Lee Chapter 1. Introduction: Discounted Cash Flow Method 17 Holden et al. text (cont.) Evaluating Forecast Accuracy: Unbiasedness: A t =  +  F t + u t (expect  = 0 and  = 1) MSE = variance(error) + mean(error) 2 MAE = mean absolute error =  t | A t – F t | / n MAPE = mean absolute percentage error Out-of-Sample Turning Points : Theil statistics: U1, U2, and 1 = UM + UR + UD Comparing 2 sets of Forecasts: d t =  1 +  2  {s t – mean(s)} + u t Non-Parametric Tests: Sign and Rank tests