Lecture_2_2010

Lecture_2_2010 - E4729 Foundations of Finance Lecture 2...

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E4729 Foundations of Finance Lecture 2 Financial Analytics July 9, 2010 Leo M. Tilman L.M.Tilman & Co. & Columbia University
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Valuation of Riskless Securities
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3 E4729 Foundations of Finance Discounting & Compounding Key Concepts Cash flow, term, interest rate (nominal vs. real rates) Compounding Discounting * PV = Present value; FV = Future Value n r CF PV ) 1 ( n r CF FV ) 1 ( * CF CF FV PV 1+r
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4 E4729 Foundations of Finance Compounding Re-invest Annually: Re-invest Semiannually: is annual rate with annual compounding is semiannual rate with semiannual compounding is Annual rate with semiannual compounding n A r CF FV ) 1 ( * n s r CF FV 2 ) 2 1 ( * A r 2 S r S r
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5 E4729 Foundations of Finance Compounding General Formula: M=1. Annual compounding M=2. Semiannual or “Bond-Equivalent” compounding M=4. Quarterly compounding M=12. Monthly compounding (e.g., mortgage) Continuous Compounding: * t=n is total time until the cash flow in years n M M r CF FV ) 1 ( * rt e CF FV
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6 E4729 Foundations of Finance Option-Free Bonds Face amount or Principal or Par Value (P) = total $ promised to be repaid Term (T) or Maturity or Time to Maturity = total length of the security in years Annual Coupon (C) = % of Face payment per year Present Value (PV) = discounted value of all cash flows P + C T C
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7 E4729 Foundations of Finance Option-Free Bonds Face amount or Principal or Par Value (P) = total $ promised to be repaid Term (T) or Maturity or Time to Maturity = total length of the security in years Annual Coupon (C) = % of Face payment per year Present Value (PV) = discounted value of all cash flows T r P C r C r C PV ) 1 ( ... ) 1 ( ) 1 ( 2 T BE BE BE r P C r C r C PV 2 2 ) 2 / 1 ( 2 / ... ) 2 / 1 ( 2 / ) 2 / 1 ( 2 / Annual Semiannual
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8 E4729 Foundations of Finance Option-Free Bonds The single discounting rate above is YIELD TO MATURITY : This equation is applicable to all cash flows, not just bonds: Yield is often referred to as “Internal rate of return” (IRR) • Link to equity models and P/E Mathematical features of the price/yield equation T y P C y C y C PV ) 1 ( ... ) 1 ( ) 1 ( 2 T i i i y CF PV 1 ) 1 (
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9 E4729 Foundations of Finance Option-Free Bonds Simple implications of the price/yield equation : If a bond’s market price increases, then its yield must decrease. If a bond’s market price decreases, then its yield must increase. Par : Market price = Par value Yield-to-maturity = Coupon Rate Discount : Market price < Par value Yield-to-maturity > Coupon Rate Premium : Market price > Par value Yield-to-maturity < Coupon Rate T i i i y CF PV 1 ) 1 (
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10 E4729 Foundations of Finance Fixed Income Mathematics  n i i i y CF P 1 1 Price/yield function is usually described as “positively convex”: If y + -y=y–y - P + -P > P-P - For very small changes, a linear relationships can be assumed: P + -P = P-P - )
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11 E4729 Foundations of Finance Bond Rules Price volatility is greater, the lower the coupon rate (think of zero coupon bond).
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Lecture_2_2010 - E4729 Foundations of Finance Lecture 2...

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