NYU Stern: Financial Seminar Series

1
NYU Stern Financial Seminar Series
Risk, Returns, and the CAPM

• Presented by
• Members of Beta Alpha Psi

2
Agenda

• Returns
• Introductory Statistics
• Risks
• Interest Rates
• Conclusion

3
Returns

• Arithmetic vs. Geometric
• Arithmetic (123)/32
• Geometric (123)(1/3)
• Lognormal
• Used because stock return occur in a continuous
  environment and are thus lognormally distributed
• Constant Average Growth Rate (CAGR)
• (Pt/Pt-n)(1/n)

4
Statistics Formulas
5
Sharpe Ratio, CAPM, and Beta

• Sharpe Ratio
• (Er - Rf)/s
• Capital Asset Pricing Model
• Er Rf ß (Rm - Rf)
• Beta an exposure facture which measures the
  proportion of market volatility (Systematic Risk)
  that a given asset is subject to

6
Risks

• Non-systematic Risk
• Systematic Risk
• Diversification
• Capital Allocation Line
• Capital Market Line
• Security Market Line

7
(No Transcript)
8
Interest Rates

• Interest Rate
• Real Rate Exp Inflation Default Premium
• Real The growth rate of purchasing power
• Nominal The interest rate not adjusted for
  purchasing power
• Inflation The rate at which prices are rising
• Default Bankruptcy Risk

9
Bond Yields

• Coupon Rate Annual Interest PMT Par Value
• Yield to Maturity The return you receive by
  investing today and holding until maturity
• Current Yield Coupon Bond Price
• Premium Bonds Bonds selling above par value
• Discount Bonds Bonds selling below par value

10
Grannys Bond Dilemma

• Duration
• A measure of interest rate sensitivity
• The dollar weighted average maturity of the bond
• Holding period over which bond is riskless
• Why is it important?
• Measure of the percent change in bond price given
  a 1 change in interest rates
• Measure the effective average maturity of a bond
• Immunize portfolios from interest rate risk for a
  riskless investment (matching duration)

11
Daddys Portfolio Construction

• Your father has asked you to find the best
  investment opportunity for him out on the market.
  There are only 3 securities in this market and
  there is one risk free rate.
• Given that your fathers risk tolerance is 25,
  how much would you have him invest in each
  security.

12
Daddys Portfolio Construction

• Security A E(r)15 s20
• Security B E(r)10 s13
• Security C E(r)8 s9
• Risk Free Rate E(r)4 s0
• Correlation (B,C) 0.5
• Correlation (A,C) 0.3
• Which of the following three portfolio is the
  market portfolio (i.e. the one with the highest
  Sharpe Ratio) ?
• 100 in A
• 50 in B 50 in C
• 75 in A 25 in C
• Is this the best that your father could do?

13
Questions?