For the sake of simplicity, taxes, commissions and other trading costs have
been omitted from the discussions and strategies in this discussion; these
should be taken into account when making your investment decisions. The
strategies are based on hypothetical situations and should only be considered as
examples of potential trading approaches.
Investor Expects Long-term Rates to Rise Reducing the Value of a Fixed-income Portfolio
Buy TYX calls to offset the decline in value of a fixed-income portfolio.
Investor expects rising long-term interest rates.
To offset a decline in the value of a long-term bond portfolio.
Buy TYX calls.
Recall that option prices move directly with
interest rates. When 30-year rates rise, TYX increases and calls tend to
increase in value while puts tend to decrease in value. Thus,
yield-based calls are used to protect or insure the value of a bond
portfolio against rising interest rates (when the value of the bonds
would decline.) By purchasing yield-based calls, investments can be
protected against large losses without sacrficing participation in
portfolio appreciation. However, remember that any portfolio
appreciation may be diminished by the cost of the call options.
An investor holds a portfolio of Treasury securities with a current market
value of $100,000. Its weighted average coupon is 6.50% and its weighted
average maturity is 20 years. The yield-to-maturity on the portfolio is
Because of mounting inflationary pressure in the
economy, the investor anticipates a 1% rise in interest rates over the
next three months. The 30-year Treasury yield is at 6.25%, and TYX at
62.50. To protect the value of his investments while continuing to earn
interest income on the bonds in his portfolio, the investor decides to
buy at-the-money TYX 62.50 three-month call options at a price of 1.50.
To calculate how many options are needed to protect the bond portfolio, the
following two-step procedure is needed;
- (A) First, determine by how much your portfolio will decline in value if interest rates were to
rise by 1%. A financial measure known as modified duration provides the
answer. Modified duration is a measure of a bond or a portfolio's price
sensitivity to changes in yield. It gives you an estimated percentage
change in the value of your bond portfolio for a 1% change in interest
rates. The calculation is complex, but is now available on most modern
financial calculators. If you are unable to calculate duration, consult
your financial advisor.
Assume that modified duration given the current value of the yield, maturity and coupon of the bonds in your
portfolio is 11 years. This means that a 1% increase in interest rates
will lead to a 11% decline in the portfolio value. Given a current
portfolio value of $100,000, an 11% decline would mean a loss of $11,000
resulting in a new portfolio market value of $89,000.
- (B) Determine by how much your long at-the-money TYX 62.5 calls will
increase in value following a 1% rise in interest rates. A 1% percent
rise in the 30-year yield from 6.25% to 7.25% results in a new value for
TYX of 72.50, an increase of 10 points. Therefore, each call with a
62.50 strike will be worth 10 points if the interest rate does rise to
7.25% at expiration. Each call will be worth $1,000 (10 points x $100
multiplier). The portfolio would decline $ 11,000; therefore, 11 calls
would have to be purchased. This would not be a total hedge because a
premium would have been paid for the calls.
For this example, an investor will purchase 11, three-month 62.50 calls at 1.50. These
calls will cost $1,650 (1.50 premium x $100 (multiplier x 11 calls).
The breakeven on this position is 64, the 62.50 strike price plus 1.50
call premium. At or above 6.4% interest rate (the breakeven level) the
call holder should begin to make money to offset some of the loss in the
Settlement Value at Anticipated Level (72.50):
The holder would exercise his calls and receive the difference between the
strike price and the settlement value. The profit would be the
difference less the premium paid. This money would be used to offset
some of the loss in the bond portfolio.
- Settlement Value: 72.50
- Less Strike Price: -62.50
- Difference: 10
- Amount Paid to Holder(10 x $100 x 11 contracts):
- Less Cost of Calls:-1,650
- Profit: $9,350
The profit on the option trade is applied to the
bond portfolio to offset some of the loss which would occur when
interest rates rose.
Settlement Value Above Breakeven (64):
If the 30-year Treasury bond yields do rise and the settlement value for
TYX is at 68 at expiration (interest rates at 6.8%), the TYX 62.50 call
option would be exercised, the holder of the calls would receive the
amount by which the closing yield exceeds the strike price. This money
would partially offset the loss in the bond portfolio due to an increase
in interest rates.
- Settlement Value: 68
- Less Strike Price: -62.50
- Difference: 5.50
- Amount Paid to Holder(5.50 x $100 x 11
- Less Cost of Calls: -1.650
- Profit: $4,400
Settlement Value Between Call Strike Price
(62.50) and Breakeven Level (64):
If by expiration the 30-year
Treasury yields do slightly increase to 6.35 which equals a settlement
value of 63.5, the holder would exercise his options. He would receive
the amount by which the settlement value is above the strike price. The
amount received would be less than what was originally paid, but it
would offset some of the cost. The value of the bond portfolio should
have only dropped slightly.
- Settlement Value: 63.50
- Less Strike Price: -62.50
- Difference: 1
- Cost of Calls: $1,650
- Less Amount Paid to Holder(1x$100x 11
- Loss: 550
Settlement Value At or Below Call Strike
If the settlement value is at or below 62.50,
the yield on the 30-year Treasury is at or below 6.25%, the holder would
have lost the total premium of $1,650, in this example. However, no
matter how low interest rates decline, the most that the option can lose
is the premium paid.
Risks In Tracking
example assumes that the yield of your bond fund moves one-for-one with
the 30-year Treasury bond yield. The risk in the combined position (bond
portfolio and calls) is that an increase in the interest rate driving
the bond portfolio is not offset by an equivalent increase in the
30-year Treasury bond yield.
Under these circumstances, the
gains in the option position may not offset the losses in the bond
position. The maximum loss in the combined position could equal the
entire premium plus the loss in the bond investment.
this "tracking error" can result in a profit if the underlying
increases more than the yield driving your investment. The greater the
similarity between the characteristics of your investment and long-term
Treasuries, the more closely the two yields are likely to track one