The Simple Math: How a Mere Quarter-Percent Interest Rate Hike Can Produce Big Swings on Bond Prices and Foreign Exchange Rates

© 2015 Prof. Farok J. Contractor, Rutgers University

Janet Yellen Agonistes

Bah! Humbug! What can a mere quarter-percent hike in the Federal Reserve Bank’s interest rate do to markets? It seems so small a change as to be trivial.

For two years prior to Janet Yellen’s appointment as Chair in January 2014, her predecessor, Ben Bernanke, and the business press speculated on the timing of a rate hike with casuistic verbal contortions that kept the markets guessing. Finally, the agony was over on December 16, 2015. After almost a decade, the Fed raised short-term interest rates by . . . a mere one-quarter percent.

But what was the agony all about? The millions of words in the media, the roiling of markets worldwide?

A Multiplier Effect on Bond and Exchange Markets

Even a one-quarter percent increase can have a much larger impact on bond markets and foreign exchange rates. The math examples below abstract from many other market considerations, including the time value of money, the length of the bond when the principal amount would be returned, and forward exchange rates, but will suffice to explain the multiplier effect in simple terms.

BOND MARKET EXAMPLE

Imagine that Investor A owned, prior to December 2015, a bond yielding 1.5% and that a new Investor B purchased, after December 2015, a bond yielding 1.75%:

• Investor A: Before December 2015, a $10,000 deposit would have been yielding the owner 10,000 (.015) = $150 per year in interest.

• Investor B: After December 2015, with a quarter-percent interest rate increase, a new investment of $10,000 would yield $10,000 (.0175) = $175 per year.

With bonds being traded in the market, which now expects a 1.75% return (as against the old 1.5% return), Investor A’s bond could now lose value by up to $1,250. This is because after December 2015, an investment of only $8,571 would yield 8,571 (.0175) = $150 in interest per year.

The face value of Investor A’s investment of $10,000 would therefore be devalued in the bond market (by other new or later investors like Investor B, who are now targeting a 1.75% return) to as low as $8,571.

Hence a mere one-quarter percent interest rate jump could devalue a bond by as much as 14 percent: (10,000 – 8,571)/10,000 = 0.1429, or a drop of up to 14.3 percent in face or resale value.[1]

EXCHANGE MARKET EXAMPLE

Imagine that Frenchman Pierre had invested, prior to December 2015, in US bonds. Assume for simplicity’s sake that the exchange rate prior to December 2015 was €1 = $1.10.

Before December 2015: A €10,000 investment by Monsieur Pierre would have converted into dollars 10,000 (1.10) = $11,000, which Pierre used to purchase US bonds yielding 1.5 percent annually (this return compares favorably with similar-grade investments in Europe):

[11.000 (.015)] = $165 in interest annually.

$165 converted back into euros would yield 165/1.10 = €150 . . . or an expected 1.5% yield for investor Pierre.

After December 2015: If exchange rates remained the same, Investor Pierre would continue to receive the same $165, or €150—a 1.5% rate of return in interest.

However, many other new investors, such as Monsieur Quentin, could earn a 1.75% return after December 2015 if the exchange rate did not change and remained at €1 = $1.10:

• An investment of €10,000 (1.10) = $ 11,000.

• $11,000 (0.0175) = $192.50 in interest.

• $192.50 converts back into 192.50/1.10 = €175, assuming exchange rates do not change.

HOWEVER . . .

Seeing the higher returns available after December 2015, yet other French investors, such as Monsieur Raymond, and a great many many others, would be eager to participate in the game. As a first step, in order to invest in the US bond market, euros have to be sold (supplied to the exchange market) and dollars purchased (or demanded in the foreign exchange market). Foreigners cannot invest in US dollar instruments unless they first exchange their own money for the US dollar in the foreign exchange market. This collective extra demand for the US dollar, from a host of foreign investors, would drive up its exchange rate. Recall that the world has a trillion dollars equivalent, or more, in liquid assets looking for a higher return.[2] Billions of euros are ready to be sold and dollars demanded, each day, if the prospect of a higher return exists. Collective higher demand for any free-floating currency such as the US dollar can drive up its value in milliseconds or minutes, from €1 = $1.10 to say €1 = $1.0209. (This 1.0209 new exchange rate is only an example—one among many scenarios of a stronger dollar.)

Hence, after the dollar strengthens in the exchange market:

• An investment of €10,000 (1.0209) = $10,209 from the currency conversion at the new exchange rate.

• $10,209 (0.0175) = $178.66 in interest earned.

• Assuming the dollar remains at the appreciated (stronger) exchange rate, $178.66 converts back into 178.66/1.0209 = €175, which is the same targeted €175—but now illustrated with a devalued euro or a strengthened or appreciated US dollar.

The euro can then have devalued from $1.1000 to $1.0209, or more than seven percent. A mere one-quarter percent hike in US interest rates can cause the euro to devalue by seven percent, as an example.

Simple Math Examples Obscure Many Complications—But Still Reflect Basic Facts

Actually, many other considerations and motivations influence investors in bond and exchange markets. For instance, the euro could devalue even more than the seven percent illustrated above if French or European investors are content to earn less than 1.75%. After all, recall that Monsieur Pierre was content to accept a return of only 1.5% prior to December 2015. What the simple examples above do not incorporate is the fact that a devalued euro also potentially changes (for the European investor) the re-conversion of the principal invested into euros, on the maturity of the bond, and not just the interest earned on the bond. For that we would need to do more complicated math involving the time value of money.

Nevertheless, the above simple examples do illustrate how a mere one-quarter percent interest rate hike by the US Federal Reserve Bank can cause much larger swings in the bond and foreign exchange markets. How important is the dollar-euro exchange rate? In 2014, US–EU trade (imports + exports in goods and services) exceeded $800 billion.[3] Transatlantic investments amounted to hundreds of billions more. To say that the international business relationship between the US and the EU is enormous is a gross understatement. Similarly, the US’ business with China and other countries is also directly affected by the strength or weakness of the dollar.

Small shocks or changes in US interest rates ripple outward to the rest of the world. Janet Yellen and her colleagues were right in agonizing so long and hard.

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[1] This is an over-simplified example because it does not incorporate the principal on maturity and the time value of money. However, it serves to make the point that a tiny change in interest rate expectations can make a large difference in the value of the bond.

[2] See my September 11, 2015 post Capital Outflows from China and the Hidden Story in China’s FDI Statistics.

[3] US Census Bureau. Trade in Goods with European Union.

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