FIXED INCOME SECURITES
LECTURE OUTLINE: TAXES TWO
PROFESSOR DAVID T. BROWN
WARRINGTON COLLEGE OF BUSINESS
UNIVERSITY OF FLORIDA
Overview.
This lecture note discusses the tax consequences of realizing capital gains and losses in a fixed
income portfolio. This note provides and intuitive discussion of the issues and explanation of
how to use the “Gains and Losses Calculator” which is a spread sheet model that can be accessed
from the class web site.
The tax consequences of realizing capital gains and losses is examined in the context of an
actively managed bond portfolio. The following lays out the basic idea for the case of an investor
that is holding a bond that is selling at a premium to the purchase price and for the case of an
investor that is holding a bond that is selling at a discount to the purchase price.
When a bond in an investor’s portfolio is selling at a premium to the purchase price, selling the
bond results in the realization of an imbedded capital gain. Thus, selling the bond forces the
investor to pay a capital gain on the security that she would not realize if she held the bond. If the
portfolio is passively managed and there is no need to sell the bond to fund a liability, then it
would be foolish to sell the bond and pay taxes that would not need to be paid. However, an
active portfolio manager might think that the bond is overvalued or has found a bond that she
thinks is undervalued. In this case, the investor needs to be comfortable that the trading
opportunity is sufficiently lucrative that it justifies the realization of a capital gain.
The calculator is designed to capture a fairly important wrinkle in this problem: the holding
period of the premium bond that the investor has in her portfolio. If the investor knows that she
will be forced to sell the premium bond in a short period of time, then the adverse tax
consequences of selling it a year early are much smaller than if the investor could hold the
premium bond until it matures.
In the case of a bond that is selling at a discount to the purchase price, selling it immediately
results in a tax deduction. The tax refund can be invested in the market, thus, if the security is
fairly priced, it would always make sense to sell the bond and harvest the loss. You might not
realize the loss today if you think the bond is undervalued or if the transactions costs of selling
the bond and buying another bond are higher than the tax savings. Again, if you know that you
are going to be forced to sell a year later, the gains from realizing the loss today are much
smaller.
The Economics in More Detail.
The following discussion refers to the situation under the “30 Year Premium Bond” tab in the
calculator. In this case, interest rates are 2% below the coupon rate on the bond you purchased.
The 8% coupon rate premium bond sells for $127.53. The best way to understand the calculator
is to consider a horse race between two investors that both hold this bond: Investor A and
Investor B. Investor A sells the bond today and buys a new par bond while Investor B holds the
premium bond and sells it in the future. The calculator compares the after-tax present value of
the two investors for different holding periods. At the end of the holding period, both investors
liquidate their positions and pay all relevant taxes.
Investor A sells the bond and realizes a gain of $27.530. This results in a tax payment of
$27.53*.20 or $5.51. Thus, investor A has $122.02 in after-tax proceeds to invest in par bonds.
Investor B holds the premium bond and sells it at the expected price in Column E. Both investors
reinvest the after-tax coupons at the assumed after-tax rate.
The difference between the after-tax value of the two investors’ positions is the tax cost of
realizing the gain early. Using the calculator, if we look at a two year horizon, the tax cost of
early realization of the capital gain is $.25. If the holding period is thirty years, then the after-tax
cost is $3.14. These numbers mean that, ignoring transaction costs, you would need to argue that
this bond is $.25 ($3.14) over valued or another bond is $.25 ($3.14) under valued to rationalize
the sale of this bond if you have a one (thirty) year holding period.
Clearly, if Investor B is forced to liquidate her portfolio next year, the cost of selling the bond
today is small. She will realize a large loss next year. However, if the bond can be held until it
matures the tax consequence of selling it early (30 years early) is over $3.
Note One:
The clever student will find something troubling about the finding that the tax cost of selling the
premium bond for an investor with a holding period of 30 years is only $3.14. You would expect
that tax cost would be $5.51. The intuition behind why the savings is only $3.14 is very hard to
sell when you assume the investor sells the bond and buys a new par bond.
It is a little easier to see if you assume that the Investor A sells the bond and buys it right back
(which you really cannot do since that is a wash sale). If Investor A sold the bond and bought it
back, she would be allowed to deduct $27.53/30 or about $.92 per year because the losses could
then be amortized. The last column in the calculator shows the present value of these tax
deductions. Notice that the present value of the amortized losses is about $2. This means that
Investor A could get $2 of the $5 tax bill paid at the sale back over time. Thus, the real cost of
early loss recognition is only about $3.
Likewise, if a discount bond is sold early you get a big loss. However, if you buy the bond back,
you need to amortize the gain over time, thus, the savings is smaller than you would guess at first
blush.
Note Two:
This calculator can also be used to evaluate the tax savings of selling bonds at a discount prior to
maturity. If you change the coupon rate on the premium bond to 4%, it sells at a price well below
$100 and a loss can be realized. The tax cost becomes a negative number – i.e. there is a tax
savings associated with selling the bond. You would not sell the bond only if you thought the
bond was undervalued by an amount larger than the tax savings.