Malkiel's Theorems for Bond Valuation

Burton Malkiel's theorems regarding bond valuation summarize the relationship between Bond prices, Yields, Coupons and Maturity period.

Hello Readers,

So today we will discuss the 5 theorems given by Mr. Burton Malkiel (Author of ‘A Random Walk down Wall Street’) regarding Bond valuation.

Theorem 1 : Inverse Relationship between Bond prices and Interest Rates

Bond prices move inversely with interest rates in the economy. So, when the yield (it may be thought of as the compounded rate of return on a bond if bought at current price and held till its maturity) on a bond increases, its price is expected to go down soon.

To simplify one may apply the formula of FV=PV(1+r)ⁿ

So if we tweak it a bit, PV=FV/(1+r)ⁿ

PV - Current price of bond

FV - Future expected price of the bond calculated by discounting its future coupons and redemption value at an appropriate rate.

r = yield

n - time to maturity

Hence if r increases FV will decrease leading to a decrease in PV i.e. current price of a bond and vice versa.

Theorem 2 : Long term bonds are riskier than short term bonds due to interest rate risk

Prices of Bonds with a long term maturity are more sensitive to interest rate risk as compared to short term bonds. Interest rate risk is the possibility that fluctuations in interest rates will lead to losses in the value of bonds.

Essentially this theorem combined with the previous one suggests that one should invest in long term bonds when interest rates are expected to fall (obviously before the Yields actually fall) and vice versa.

Theorem 3 : Sensitivity at decreasing rate

The sensitivity of a bond’s price to interest rates increases with its maturity but the increase occurs at a decreasing rate.

Theorem 4 : Lower the coupon rate (i.e. interest rate on the bond) riskier the bond is.

Lower the coupon rate on the bond, the increased risk for an investor of getting back his investment along with the promised interest and moreover Bonds with a lower coupon are more sensitive to interest rate changes.

Theorem 5 : Asymmetrical Volatility

In simple words, Capital Gains from an Interest rate decline exceed the Capital Losses from an Interest rate increase.

I have tried to explain all the theorems through calculations int he excel file given below

SFM Bond Valuation.xlsx

Hope you found it to be helpful,

Will see you soon with another write up.