Introduction to Investment Planning Virtual Class 2 of 3

1. Introduction to Investment PlanningVirtual Class 2 of 3 Asset Pricing Models, Portfolio Management, Investment Returns, Time Influence on Security Valuation, Formula Investing, Asset Allocation and Portfolio Diversification.

2. Asset Pricing Models • Option Pricing Models • Arbitrage Pricing Theory • Behavioral Asset Pricing Model (BAPM) • Capital Asset Pricing Model (CAPM)

3. Option Pricing Models • Binomial Option Pricing Model (BOPM) • Put-Call Parity • Black-Scholes-Merton

4. Binomial Option Pricing Model • Can only be used for European options • Will not be tested on the calculation – a general awareness is all that is academically required • Option value is determined by summing the “up” value times the “up” probability with the “down” value times the “down” probability • The “up” value is a forecasted ending stock price less the strike price • The “down” value is a forecasted ending stock price less the strike price

5. Put-Call Parity • Important to know for real world applications • Only applies to European options • No need to memorize the formula. You will not be tested on this concept • C - P = S - PV(X) Where C = Value of Call Option P = Value of Put Option S = Value of Underlying Stock PV(X) = Present Value of Strike Price

6. Black-Scholes-Merton • Only applies to European options • Complicated formula – you will not be tested on this • The 2 basic variables (5 expanded variables) that determine an options price are: • Intrinsic value of option • Underlying price of stock • Strike price of option contract • Time premium • Risk-free rate of interest • Time to expiration • Volatility of underlying stock (measured by SD)

7. Arbitrage Pricing Theory • Multi-factor model • Attempts to accommodate sudden changes in macro events such as inflation, interest rates, etc. • Model can be summarized as “expect the unexpected”

8. Behavioral Asset Pricing Model (BAPM) • Importance of Behavioral Finance is growing • Basic premise is that investors are human and are value expressive • Behavioral Finance is a direct contrast to CAPM, Black-Scholes-Merton, and EMT which all assume investors are perfectly “rational” with computer-like characteristics (androids)

9. CAPM vs. BAPM Now let’s jump to the course content and view the Behavioral Asset Pricing Model as developed by Sherfrin and Statman.

10. Capital Asset Pricing Model (CAPM) • Risky assets only • “Rational” investor wants to maximize return for any given level of risk • “Rational” investor wants to minimize risk for any given level of return • Key assumptions: • An investor can borrow and lend at the same rate • The “Market” portfolio is completely diversified

11. Capital Asset Pricing Model (CAPM)

12. Utility (Indifference Curves) Utility curves are a mapping of utility. In the context of investment planning, they directly relate to investor risk aversion and risk/return preferences

13. Capital Asset Pricing Model (CAPM)

14. CAPM with Risk Free

15. CAPM in a Global Context

16. Security Market Line (SML) The SML is also known as the required return as well as the CAPM formula

17. SML Shifts with Inflation

18. SML Slope Change by Increase in Market Risk Premium (MRP)

19. CML versus SML Key differences: • CML is reserved for efficient portfolios – SML can be used for any portfolio • CML uses standard deviation as a measure of risk – SML uses Beta • Assets cannot exist above the CML – SML can have assets above the line in an ex post context

20. Investment Statistics • Standard Deviation • Coefficient of Variation • Correlation Coefficient • Covariance • Coefficient of Determination (R ) • Standard Deviation of a Two-asset Portfolio • Beta 2

21. Standard Deviation Standard Deviation is a measure of a security’s or a fund’s total risk (both systematic and unsystematic). It is a measure of VARIABILITY. That is, how much variation one can expect in the actual return versus the expected return. Example: ABC stock has had the following returns over the last four years: 12%, 18%, -2%, and 6%. Calculate the expected return and standard deviation based on this historical data.

22. Standard Deviation Example: ABC stock has had the following returns over the last four years: 12%, 18%, -2%, and 6%. Calculate the expected return and standard deviation based on this historical data. KeystrokesThe calculator displays: 12 Σ+      1.00 18 Σ+ 2.00 2 CHS Σ+ 3.00 6 Σ+ 4.00 gx(the zero key)          8.500 (this is the mean) gs(the decimal key)      8.544 (standard deviation)

23. Coefficient of Variation A measure of portfolio efficiency. That is, how much risk is incurred for any given level of return. The Formula is: CV = SD X

24. Coefficient of Variation Conclusion: Security A - for every unit of return, which there were 8, I have 1.25 units of risk. Security B - for every unit of return, which there were 5, I have 1.40 units of risk. Therefore, Security B obtained its return by incurring much more risk. Example: Security A Security B 8% 10% 10 8 1.25 5% 7% 7 5 1.40 Return Standard Deviation CV = CV =

25. Correlation Coefficient • Usually expressed as “r”, the statistic ranges from -1.0 to +1.0 • Measures the degree of movement between two assets • -1.0 is perfectly negative • +1.0 is perfectly positive • Correlation of 0.00 is no correlation or random correlation (sometimes the assets move together and sometimes move apart).

26. Covariance • Refinement of correlation between securities taking security risk into account. • COVAB = SDA × SDB × rAB • Required as an input into the Standard Deviation of a Two-asset Portfolio formula • Okay to use whole numbers for standard deviations as long as you use whole numbers for standard deviations in the Standard Deviation of a Two-asset Portfolio formula

27. 2 Coefficient of Determination (R squared) • Simply the correlation coefficient squared

28. 2 Coefficient of Determination (R squared) • Simply the correlation coefficient squared • The result of linear regression, R measures the relationship between an independent variable (the market or the most appropriate benchmark) and a dependent variable (the stock). 2

29. 2 Coefficient of Determination (R squared) • Simply the correlation coefficient squared • The result of linear regression, R measures the relationship between an independent variable (the market or the most appropriate benchmark) and a dependent variable (the stock). • Specifically, how much variation in the dependent variable (stock) is caused by the variation in the independent variable (market). 2

30. 2 Coefficient of Determination (R squared) • Simply the correlation coefficient squared • The result of linear regression, R measures the relationship between an independent variable (the market or the most appropriate benchmark) and a dependent variable (the stock). • Specifically, how much variation in the dependent variable (stock) is caused by the variation in the independent variable (market). • (1 – R ) serves as a proxy for unsystematic risk 2 2

31. 2 Coefficient of Determination (R squared) • Simply the correlation coefficient squared • The result of linear regression, R measures the relationship between an independent variable (the market or the most appropriate benchmark) and a dependent variable (the stock). • Specifically, how much variation in the dependent variable (stock) is caused by the variation in the independent variable (market). • (1 – R ) serves as a proxy for unsystematic risk • Only appropriate to use Beta (or anything that uses Beta – Treynor, Alpha) when the R is close to 1.0 2 2 2

32. Correlation Coefficient

33. Standard Deviation of a Two-asset Portfolio • If two assets have perfect positive correlation, then and only then, can you determine the standard deviation of the portfolio via a simple weighting of the two assets • Any correlation less than +1.0 will lead to diversification benefits Now let’s jump to the Calculator Keystrokes page located within your online modules.

34. Beta • Beta is a special type correlation coefficient, regressed between the asset and the market • Market, by definition, has a Beta of 1.0 • Betas greater than 1.0 are more volatile than the market • Betas less than 1.0 are less volatile than the market (said to be “defensive”) • Readily available statistic, probably will not have to calculate • Only appropriate to use if a portfolio has a high R 2

35. Performance Indices • Sharpe Ratio • Treynor Ratio • Alpha (Jensen's Alpha) • Information Ratio All of these formulas are on the CFP Board’s formula sheet

36. Sharpe RatioPerformance Index • Sharpe Index is a relative measure • Numerator is known as “excess returns” (Realized Return minus Risk Free) • Denominator is the Standard Deviation of the asset • The higher the number, the better return/risk relationship • The appropriate performance index when R is low because it measures total risk 2

37. Treynor RatioPerformance Index • Treynor Index is a relative measure • Numerator is known as “excess returns” (Realized Return minus Risk Free) • Denominator is the Beta of the asset • The higher the number, the better return/risk relationship • Only appropriate to use when the R is sufficiently high (close to 1.0) because it only measures systematic risk 2

38. Jensen’s AlphaPerformance Index • Jensen’s alpha is an absolute measure • It is the Realized Return minus the Required Return • If Realized Return is > than the Required Return, then alpha is positive • If Realized Return is < than the Required Return, then alpha is negative • If Realized Return is = to the Required Return, then alpha is zero

39. Security’s Performance Vs. the Security Market Line (SML)

40. Information RatioPerformance Index • Information Ratio, also known as the appraisal ratio, is a relative measure • You will probably not have to calculate this although it is important to understand • Numerator is known as “alpha” (Realized Return of asset minus the Realized Return of a preselected benchmark) • Denominator is the Standard Deviation of the excess returns (alpha), not the standard deviation of the underlying asset

41. Measures of Investment Returns • Holding Period Return (HPR) • Geometric Returns (Time Weighted) • Internal Rate of Return (IRR) (Dollar Weighted) • Dollar Weighted Vs. Time Weighted • Yield to Maturity (YTM) • Yield to Call (YTC) • Realized Compound Yield (RCY) • Macaulay Duration • Modified Duration • Convexity and Duration • Relating Duration to Bond’s Price

42. Holding Period Return P - P + D • Not Indexed for Time Value of Money (TVM) • Formula has two components: • Capital Appreciation Component • Income Yield Component • Formula assumes that Dividends are not reinvested E B P B P - P E B P B D P B

43. Sample Question # 1 The holdings of your client are as follows: ANNUAL JUNE 30, 2008 JUNE 30, 2009 INVESTMENT * INCOME PURCHASE $ MARKET PRICE Money Market $ 6,500 $ 100,000 $ 100,000 11% T bonds $ 11,000 $ 100,000 $ 140,000 S&P Index Fund $ 6,000 $ 100,000 $ 160,000 Computer Fund $ 3,000 $ 100,000 $ 85,000 * There have been no capital gains distributions. During the 12 months from June 30th, last year, through June 30th, this year, the portfolio earned, in annual yield and before-tax appreciation, respectively: A. 5.5% and 17.5% B. 5.5% and 21.3% C. 6.6% and 17.5% D. 6.6% and 21.3%

44. Sample Question # 1 The holdings of your client are as follows: ANNUAL JUNE 30, 2008 JUNE 30, 2009 INVESTMENT * INCOME PURCHASE $ MARKET PRICE Money Market $ 6,500 $ 100,000 $ 100,000 11% T bonds $ 11,000 $ 100,000 $ 140,000 S&P Index Fund $ 6,000 $ 100,000 $ 160,000 Computer Fund $ 3,000 $ 100,000 $ 85,000 * There have been no capital gains distributions. During the 12 months from June 30th, last year, through June 30th, this year, the portfolio earned, in annual yield and before-tax appreciation, respectively: A. 5.5% and 17.5% B. 5.5% and 21.3% C. 6.6% and 17.5% D. 6.6% and 21.3% Rationale: $26,500 income/ $400,000 Purchase, $85,000 appreciation/$400,000

45. Geometric Return Now let’s jump to the Calculator Keystrokes page for a review of this calculation.

46. Internal Rate of Return (IRR) (Dollar Weighted) • “Magic” rate that equates the cash outflow at time zero with the present value of all future cash inflows • By definition, the IRR is the rate that would make the Net Present Value (NPV) = 0 • Also known as a Dollar Weighted Return, it is appropriate to use for a particular client based on the client’s unique timing of inflows and outflows from the investment • Flawed reinvestment assumption • YTM and YTC are examples of IRR

47. Internal Rate of Return (IRR) (Dollar Weighted) Now let’s jump to the Calculator Keystrokes page for a review of this calculation.

48. Dollar Weighted Return versus Time Weighted Return • Time Weighted Return is a global standard for fund performance • Time Weighted Return is based solely on the appreciation or depreciation in the fund from period to period • Dollar Weighted is appropriate for a specific client with their own particular cash flows • Dollar weighted return does account for when (and at what price level) investments are made and when withdrawals occur

49. Dollar Weighted versus Time Weighted Example Investment Advisor “A” Investment Advisor “B” $ + $ $ - $ $ + $ $ - $ Initial Investment Year 1: Market up 50% Each Advisor up 50% Subtotal (end of year 1) Additional Investment Year 2: Market down 50% Each Advisor down 50% Subtotal (end of year 2) 100,000 50,000 150,000 1,000,000 575,000 575,000 1,000,000 500,000 1,500,000 100,000 800,000 800,000

50. Dollar Weighted Results Investment Advisor “A” Time 0 Time 1 Time 2 (100,000) (1,000,000) 575,000 HP 12C Keystrokes 100000 CHSgCF0 1000000 CHS gCFj 575000 gCFj fIRR Answer = -45.47%