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Risk and Return Measures - Duration, Convexity and Capitalized Earnings

  1. Duration and Convexity
    1. Duration - the weighted average term to maturity of a bond's cash flows. In common parlance, duration serves as an approximation of how quickly a bond holder is repaid. All else being equal, bonds with longer maturities and lower coupons have a longer duration. Longer duration bonds fluctuate more widely in response to a change in interest rates than do shorter duration bonds. The formulas appear below:

Exam Tips and Tricks
duration= -%
Δ Bond Price/Yield %Δ where Δ=change
Percentage price change=-duration x (yield change in %)


    1. Convexity - measures the degree of curvature in the price/yield relationship, accounting for the amount of error in price estimation. For a straight bond, the price increases more with a decline in yields than it decreases when yields increase.
  1. Capitalized Earnings - this is a rudimentary valuation tool. A company's earnings are divided by its cost of capital. Disadvantages to this formula include the imprecision of earnings due to adjustments, the proper selection of the firm's cost of capital to reflect inflation, risk and other factors relevant to the nature of the firm and its industry and the failure of the formula to consider any residual asset value at the end of the term. The formula is used to value perpetuities, preferred stock and real estate (direct capitalization, where earnings are Net Operating Income, income less fixed and variable operating expenses before depreciation and mortgage debt service).


Exam Tips and Tricks
V = E/R
Where: V=the company\'s value; E=earnings used to value the firm; R=the discount rate

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