**Silicon Valley Bank** could easily have avoided its mark-to-market write-down and bankruptcy. Its managers**,** their outside consultants, and the **steward of the banking system** – the Federal Reserve Bank – should all have been required to read, understand, confirm and apply the constraints immanent in **Burton Malkiel’s** five theorems, **especially Theorem 2,** in his 1962 essay:

Malkiel, Burton,** Expectations, Bond Prices, and the Term Structure of Interest Rates**, Quarterly Journal of Economics Vol. LXXVI (May 1962) pp. 197-218 (Cambridge, Mass.: Harvard University Press) [

**Malkiel, 1962**]:

In the essay’s Section II, **THE MATHEMATICS OF BOND PRICES**, Malkiel explains that the **market price, P,** of a bond, is determined by

**four factors**: 1) the face value,

*, or the principal amount to be paid at maturity, 2) the bond’s coupon or interest paid periodically,*

**F****3) the effective interest rate per period,**

*C,***and 4) the number of years to maturity,**

*i,**Malkiel:*

**N.***P = C/(1+i) + C/(1+i) ^{2} + …+ C/(1+i)^{N} + F/(1+i)^{N}*

^{ }Summing the geometric progression and simplifying, we obtain

*P = C/i[1 – 1/(1+i) ^{N}] + F/(1+i)*

^{N }

^{ }or,

*P = C/i + (F – c/i)/(1+i) ^{N}*

Malkiel’s **five theorems** treat the prices, absolute changes in prices, and the percentage changes in prices due to the factors of yield* i,* change in yield

*, and relevant term to maturity*

**δi****. Using the calculus of differentiating, Malkiel**

*N***proves each of the five theorems**immediately after he states them. We will simply state each theorem and leave it to the serious student to study, understand, and confirm the differentiations constituting Malkiel’s proofs.

**Theorem 1**: Bond Prices move inversely to bond yields.

**Theorem 2**: For a given change in yield from the nominal yield, **changes in bond prices are greater, the longer is the term to maturity**.

**Theorem 3**: The percentage price changes described in **Theorem 2** increase at a diminishing rate as N increases.

^{ }**Theorem 4**: Price movements resulting from equal absolute (or, what is the same, from equal proportionate) increases and decreases in yield are asymmetric; i.e. a decrease in yields raises bond prices more than the same increase in yields lowers prices.

**Theorem 5**: The higher is the coupon carried by the bond, the smaller will be the percentage price fluctuation for a given change in yield except for one-year securities and consols.

Also, relevant to recent mistakes or oversights by bank management and the Central Bank, we quote **Schumpeter** re** the responsibility of the banking system**:

Banks are not there to “force their money upon people,”^{4 }nor “do they congratulate themselves if they are *loaned* up.”^{5} A banking committee is not “an automaton” but **understanding and attentive to purpose and situation**, “ judging chances of success of each purpose and, as means to this end, the kind of man the borrower is, watching him as he proceeds …”^{6} “It should be observed how important it is for the system of which we are trying to construct a model, that the banker should know, and be able to judge, what his credit is for and that he should be an **independent agent**. To realize this is to understand what banking means.”^{7} “the banker’s function is essentially a **critical, checking, admonitory** one. **Alike in this respect to economists, bankers are worth their salt only if they make themselves thoroughly unpopular with governments, politicians and the public.** This does not matter in times of intact capitalism. In the times of decadent capitalism, this piece of machinery is likely to be put out of gear by legislation.”^{8 }McShane, Philip (quoting Joseph Schumpeter’s Business Cycles I and II) *Implementing Lonergan’s Economics*, in *The Lonergan Review, Culture Science and Economics*, Vol. III, No 1, Spring 2011, Seton Hall University, pp. 196-204