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Fin 525 Week 3. Treasury Bills and Treasury STRIPS . More About Gold: There are Many Ways to Own It. Physical form Bars Coins Jewelry Warehouse receipts Forward contract Futures contract ETF (Exchange-Traded Fund). Forward Contracts vs. Futures Contracts. Forward contract

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Fin 525 Week 3


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fin 525 week 3

Fin 525 Week 3

Treasury Bills and Treasury STRIPS

more about gold there are many ways to own it
More About Gold:There are Many Ways to Own It
  • Physical form
    • Bars
    • Coins
    • Jewelry
    • Warehouse receipts
  • Forward contract
  • Futures contract
  • ETF (Exchange-Traded Fund)

Professor Ross Miller • Fall 2006

forward contracts vs futures contracts
Forward Contracts vs. Futures Contracts
  • Forward contract
    • Agree on the price now for a transaction at a future date (no money changes hands now)
    • Generally, one side of the agreement is a financial institution and the contract cannot be traded
    • Highly customizable and often involves several millions of dollars
  • A futures contract is like a forward contract except that:
    • Both sides post “margin” to ensure that they can cover potential declines in the value of the contract
    • Futures contacts are designed to be traded
    • Futures contracts are standardized and a single contract usually involves less than $1 million

Professor Ross Miller • Fall 2006

a popular gold etf ishares comex gold trust iau
A Popular Gold ETF:iShares COMEX Gold Trust (IAU)
  • This ETF is essentially a mutual fund that holds only gold and charges an annual fee of 0.40% (which compares with 0.10% to 0.20% for the typical S&P 500 Index mutual fund)
  • One “share” conveys ownership of 1/10 of an ounce of gold
  • It has been trading since 1/21/2005
  • Other details are available via Google or the official fact sheet

Professor Ross Miller • Fall 2006

13 week and 26 week u s treasury bills
(13-week and 26-week) U.S. Treasury Bills
  • Short-term securities issued (at auction) by the U.S. Treasury to finance the national debt
  • As good as cash for many purposes
    • Margin in brokerage accounts
    • Transfer of funds between corporations
  • Extremely liquid
    • Easy to purchase electronically
    • Easy to buy and sell through brokers & dealers
    • Easy to lend to others for short periods of time (repurchase agreements or repos)

Professor Ross Miller • Fall 2006

t bill quotes from bloomberg from the afternoon of september 14 2006
T-Bill Quotes from Bloombergfrom the afternoon of September 14, 2006

Professor Ross Miller • Fall 2006

the first tricky thing about t bills their price is quoted on a discounted basis
The First Tricky Thing about T-Bills:Their Price is Quoted on a Discounted Basis
  • Suppose you had a money market security that cost $10,000 and paid $10,500 in one year
  • You would normally think of it as paying 5% annual interest
  • However, you could also think of it as being priced at a discount as such:
    • The fraction of the face (or future) value that you pay is $10,000/$10,500 = 95.24%
    • This means the security is trading at a100% - 95.24% = 4.76% (annual) discount

Professor Ross Miller • Fall 2006

some words about t bill discounts
Some Words about T-Bill Discounts
  • Professionals treat the discount as the T-Bill’s “price”
  • The actual money paid for the T-Bill moves in the opposite direction of the discounts
    • A higher discount yield means that the T-Bill costs less to purchase
    • A lower discount yield means that the T-Bill costs more

Professor Ross Miller • Fall 2006

the second tricky thing about t bills they are quoted using a 360 day year
The Second Tricky Thing about T-Bills:They Are Quoted Using a 360-Day Year
  • Suppose you have a T-Bill with 90 days until maturity that is quoted at a 4% (annual) discount
  • 90 days is ¼ of a 360-day year
  • The discount is directly pro-rated (compounding is ignored) so the discount applied to the T-Bill is ¼ of 4% = 1%
  • Hence, a T-Bill that pays $10,000 at maturity can be purchased for $9,900, which is a discount of 1% to its face (or future) value

Professor Ross Miller • Fall 2006

old espeed t bill quotes from the wall street journal subscription required
Old eSpeed T-Bill Quotes from the Wall Street Journal(subscription required)

Market Close 1/31/2006

Professor Ross Miller • Fall 2006

bid asked and ask yield on the previous slide
“Bid,” “Asked,” and “Ask Yield” on the Previous Slide
  • Bid
    • The (annual) discount for which a dealer is willing to purchase the T-Bill
  • Asked
    • The (annual) discount for which a dealer is willing to sell the T-Bill
  • Ask Yield
    • The T-Bill’s yield computed from the “Ask”

Professor Ross Miller • Fall 2006

hey professor the wall street journal can t count
Hey, Professor, TheWall Street Journal Can’t Count!
  • February 2 is 2 days after January 31, not 1 day
  • What’s Happening: If you buy a T-Bill on January 31, the trade is actually settled on the next business day
    • This is called T+1 settlement and applies to most fixed income securities, derivative securities, and mutual funds
    • For stocks, T+3 settlement is still the standard

Professor Ross Miller • Fall 2006

let s see what it costs to buy 10 000 face value of the t bill that matures in 36 days
Let’s See What It Costs to Buy $10,000 Face Value of The T-Bill That Matures in 36 Days
  • The “asked” is 4.24%
  • Based on a 360-day year, 36 days is 1/10 of a year
  • The “discount” for the bill is 1/10 x 4.24% = 0.424%
  • Applying the discount to $10,000 gives .00424 x $10,000 = $42.40
  • The final cost is $10,000 – $42.40 = $9,957.60

Professor Ross Miller • Fall 2006

what is the yield of a t bill that costs 9 957 60 and returns 10 000 in 36 days
What is the Yield of a T-Bill that Costs $9,957.60 and Returns $10,000 in 36 Days?
  • Rate of return over the period is $42.40/$9,957.60 = 0.004258 or 0.4258%
  • 36 days is not really 1/10 of a year, but 36/365 of a year, which is 0.09863
  • Dividing 0.004258 by 0.09863 gives a simple annual yield of 4.32%, which matches the “asked yield” from the Wall Street Journal
  • Note that the APY, which is not reported, will be higher

Professor Ross Miller • Fall 2006

why t bills have lower yields than eurodollars
Why T-Bills Have Lower Yields Than Eurodollars
  • T-Bills are exempt from state and local taxes
  • The U.S. Treasury is considered the least risky financial institution in the world (the top credit rating is AAA, the U.S. Treasury is considered by some to be AAAA)
  • Interest rates from Treasury securities are generally used as the “risk-free” interest rate required in some financial models; however, practitioner often use eurodollar (and interest rate swap) rates in some of their models

Professor Ross Miller • Fall 2006

the ted treasury eurodollar spread
The TED (Treasury-Eurodollar) Spread
  • The difference in yield between the three-month Eurodollar (LIBOR) and the three-month T-bill
  • The TED spread is considered a credit-risk indicator and is easy to trade with futures
  • Example from September 15, 2006
    • 3-month Eurodollar yield: 5.39%
    • 3-month (90-day) T-bill yield 4.93%
    • TED spread is 46 b.p.
    • Why? 5.39% – 4.93% = 0.46% = 46 b.p.

Professor Ross Miller • Fall 2006

repurchase agreement repo
Repurchase Agreement (Repo)
  • Deals with the problem that T-Bills are only issued every 7 days
  • To create a “custom maturity” for a T-Bill, a dealer will “rent it out” for the desired period of time, often just overnight
    • The actual mechanics are that the dealer sells the T-Bill and agrees to “repurchase” it on a specified date at a higher price
    • The “renter” is said to have a reverse repurchase agreement and has the T-Bill as collateral
  • T-Bills are not the only securities that are “repoed,” but are the most popular

Professor Ross Miller • Fall 2006

treasury strips
Treasury STRIPS
  • Stands for Separate Trading of Registered Interest and Principal of Securities and is an example of a “pure discount bond”
  • They are the principal and coupon payments “stripped” from U.S. Treasury notes and bonds
  • Treasury notes and bonds can be “reconstituted” from STRIPS
  • They generate cash flows like T-Bills; however, they can have maturities out as far as 30 years

Professor Ross Miller • Fall 2006

more on treasury strips
More on Treasury STRIPS
  • Two differences from Treasury bills
    • Quoted as a price rather than as an annualized discount
    • Even though payments are only made on maturity, taxes are assessed annually on the accrued interest
  • Often referred to as “Treasury zero-coupon bonds” or “Treasury zeroes” and treated like original-issue discount (OID) securities
  • Created in 1985 by U.S. Treasury in response to separate trading of treasury security principal and interest developed by securities firms, most notably Merrill Lynch

Professor Ross Miller • Fall 2006

the three types of strips
The Three Types of STRIPS
  • ci – Coupon Interest: Coupon payment from either a note or bond
  • np – Note Principal: Principal payment from a specific Treasury note (a Treasury security issued with a maturity of 2 to 10 years)
  • bp – Bond Principal: Principal payment from a specific Treasury bond (a Treasury security issued with a maturity of more than 10 years)

Professor Ross Miller • Fall 2006

cusips
CUSIPs
  • They are lots of STRIPS, sometimes several with the same maturity date, so there has to be an easy way to tell them apart
  • CUSIPs are unique securities identifiers that all securities (including STRIPS) are assigned
  • CUSIPs are the standard (and sometimes only) way to uniquely identify fixed-income securities
  • Although stocks, mutual funds, etc. also have CUSIPs, ticker symbols (like GOOG for Google) are more commonly used to identify them

Professor Ross Miller • Fall 2006

getting prices for strips
Getting Prices for STRIPS
  • Although easy to buy and sell from major brokers, they are difficult to get quotes for
  • Yahoo! Finance has quotes through its bond screener (simply check “Treasury Zero Coupon” and then click on the “Find Bonds” button); however, these prices are highly unreliable
  • The Wall Street Journal only prints those with maturities of ten years or less and has nothing online
  • STRIPS are usually quoted in 32nds

Professor Ross Miller • Fall 2006

quotes for 9 16 2005 from the wall street journal print edition
Quotes for 9/16/2005 from the Wall Street Journal Print Edition

Professor Ross Miller • Fall 2006

a detailed look at a strips quote
A Detailed Look at a STRIPS Quote

(Feb 06) Matures February 15, 2006

(ci) Is a coupon payment

(Bid 98:19 and Ask 98:19) Has both a bid and ask price of 98 and 19/32, which is 98.59375

(Yld 3.50) Has a yield (calculated on a bond-equivalent basis) of 3.50%

Note: The maturity price is 100

Professor Ross Miller • Fall 2006

quotes from the bottom of the 9 16 05 table
Quotes From the Bottom of the 9/16/05 Table

Professor Ross Miller • Fall 2006

general formula for valuing pure discount bonds with t years to maturity
General Formula for Valuing Pure Discount Bonds with T Years to Maturity
  • F is face value (same as the FV we used before)
  • T is time (in years) to maturity and can include fractional year—10 years and 2 months (the time until expiration for the Nov 2015 STRIPS would give T=10.1666…

Professor Ross Miller • Fall 2006

the sensitivity of strips prices to changes in interest rates
The Sensitivity of STRIPS Prices to Changes in Interest Rates
  • Like all low-risk bonds, the value of a STRIPS goes down when interest rates increase and goes up when they decrease
  • As the time to maturity (T) of a STRIPS increase, so does its sensitivity to changes in interest rates
  • This is a direct consequence of the formula for the pure discount bond formula—higher values of T means bigger changes in PV for the same change in r

Professor Ross Miller • Fall 2006

calculating the pv for a strip with r 4 43 and t 10 1666
Calculating the PV for a STRIP with r = 4.43% and T = 10.1666

PV = F/(1+r)T = 100/(1+0.0443)10.1666

= 100/1.5538 = 64.36

Notice that this does not match the ask price of 64:04, which is 64 4/32 or 64.125. This is because yields on STRIPS are quoted so that they are comparable to bonds that pay interest semi-annually

Professor Ross Miller • Fall 2006

the rule of 72
The Rule of 72
  • For zero-coupon bonds with “normal” interest rates, the time it takes to double money is approximately 72 divided by the interest rate in percentage terms
  • Examples of this “rule”:
    • At a 10% APY, it takes about 7.2 years for money to double
    • Conversely, if you want your money to double in 10 years, you need to receive an APY of approximately 7.2%

Professor Ross Miller • Fall 2006

the gotcha with strips
The “Gotcha” with STRIPS
  • STRIPS would appear to be an ideal tax shelter—no taxable interest, just a giant capital gain at maturity
  • The IRS figured this angle out some time ago
    • All OIDs (original-issue discount bonds) have their discount amortized over the life of the bond
    • This is the worst of both worlds, the only cash flow you get is at maturity, but you are taxed on annual basis for cash you do not receive
  • STRIPS are mainly useful for tax-sheltered or foreign investments

Professor Ross Miller • Fall 2006

why strips are so important
Why STRIPS are So Important
  • Using STRIPS, financial institutions can create risk-free securities with any sequence of cash flows that they or their clients desire
  • There are other ways to approximate securities using duration and convexity analysis (we will get to this), but STRIPS replicate risk-free cash flows exactly

Professor Ross Miller • Fall 2006

the hey you never know case
The “Hey, You Never Know” Case
  • Your challenge: Choose a Jackpot Prize Payment Option
  • Your (second) challenge: Write a question that will help you make a more informed choice
  • You may assume that the winner is roughly 30 years old with both unexceptional income and wealth

Professor Ross Miller • Fall 2006

constructive receipt
Constructive Receipt
  • The IRS taxes any income once it is available
    • You cannot avoid declaring income by not cashing a check
    • You cannot ask a client simply to pay you later for services already rendered
    • You cannot conveniently forget to ask a client for payment
  • The same principle applies to the lottery
    • “Under the doctrine of constructive receipt, the winner of a prize who is given the option at the time the prize is won of receiving either a single cash payment or an annuity, is required to include the value of the entire single cash payment in gross income, even if the annuity option is exercised.” (CPA Journal link at the top of this page)
    • The way around this rule is the payment option selection at the top of the lottery ticket

Professor Ross Miller • Fall 2006

determination of nys lotto lump sum
Determination of NYS Lotto Lump-Sum
  • Calculated in a spreadsheet using broker quotes for Treasury STRIPS (the initial cash payment is excluded)
    • The above link works if you ignore the request for an account and password and simply click OK whenever prompted
  • Note that the payments grow over time

Professor Ross Miller • Fall 2006

structured settlements
Structured Settlements
  • Allows legal settlements or contest prizes to be written off immediately by those making the payment and provides the recipients with customized installment payments
  • For (nontaxable) legal settlements, the major tax advantage is that the investment income goes untaxed
  • For (taxable) contest prizes, the major tax advantage is that more of the prize is taxed in lower tax brackets by spreading the payment out over several years
  • Most structured settlements are backed by STRIPs

Professor Ross Miller • Fall 2006

for week 4
For Week 4
  • Follow the links on the slides
  • Read the commentary on inflation by Caroline Baum (an alternative link appears on WebCT)
  • Read RWJ Ch. 4, pp. 75–85 and Ch. 5, pp. 106–112
  • Do the problems on the 6 slides that follow this one

Professor Ross Miller • Fall 2006

true false statements page 1 of 2
True-False Statements (Page 1 of 2)
  • As the Fed has raised the fed funds rate from 1% to 5¼%, the discount on Treasury bills has risen with it.
  • If the discount for Treasury bills used the actual number of days in a year instead of 360 days, then the discount and the yield would have the same value.
  • Doubling the maturity of a STRIPS will exactly halve its price.

Professor Ross Miller • Fall 2006

true false statements page 2 of 2
True-False Statements (Page 2 of 2)
  • A STRIPS with a longer time to maturity will generally trade at a lower price than one with less time to maturity.
  • The State of New York can save money by dividing the lottery payoff into equal payments instead of its current system of increasing payments (assume the timing of the payments remains the same).

Professor Ross Miller • Fall 2006

using the information from september 14 2006
Using the Information from September 14, 2006

For the two T-Bills given above:

  • What fraction of a “year” do they have until maturity?
  • What would it cost to buy $10,000 face value of each?
  • Show that Bloomberg calculated their yields correctly.

Professor Ross Miller • Fall 2006

funding future purchases with strips
Funding Future Purchases with STRIPS

A local public radio station has decided to mount a special one-day pledge drive to fund improvements for its broadcast facilities. It wants to but a new transmitter one year after the pledge drive, new studio cameras two years after the pledge drive, and a remote broadcast van three years after the pledge drive. The projected prices of this equipment are as follows:

Transmitter at the end of Year 1: $35,000

Cameras at the end of Year 2: $16,000

Remote broadcast van at the end of Year 3: $28,000

Professor Ross Miller • Fall 2006

funding future purchases with strips continued
Funding Future Purchases with STRIPS(continued)

The station’s treasurer, who formerly worked for the state lottery, decides that the station should put the proceeds from the fund drive immediately into U.S. Treasury STRIPS to fund the three planned purchases. During the pledge drive, he receives the following quotes from his broker:

1-year STRIPS: 98.52

2-year STRIPS: 96.12

3-year STRIPS: 91.51

Professor Ross Miller • Fall 2006

funding future purchases with strips continued42
Funding Future Purchases with STRIPS(continued)
  • According to the pure discount bond formula, what must be the interest rate that is paid by the 1-year STRIPS?
  • How much will the station need to raise in the fund drive in to purchase the STRIPS required to fund the three purchases on the time-table given above?
  • Response to the pledge drive was disappointing, but the treasurer figures that the station can still fund all three items if he rearranges the order in which the three items are purchased. Assuming the prices do not depend on when each item is purchased, how much must the station now raise so that it can afford to purchase all three items?

Professor Ross Miller • Fall 2006