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2 InterestRatesBonds

Summary

  • reading
  • review
  • dcf
  • perpetuities
  • annuities
  • apr
  • compounding
  • bonds
  • irr
  • bond yields and prices

Reading Review

How can you see through wall streets ritual of wrong?

what determines the price of a publicly traded stock?

Securities, are literally anything, bond, stock, etc. They can be traded publicly and privately.

what determines the price?

Supply and demand, it's just market forces

at the end of the day, the only number that matters, is how much someone is willing to pay for that security.

what is an index in the context of financial markets?

a collection of different securities, where they are weighted by their market share. it serves as a good average value for that market.

S&P 500 is a weighted average of the prices of all of those stocks.

in the articles.

can an index be traded?

An index cannot be traded, but there is something called an index fund, where investors give them money to buy exactly the index.

Wall street firms, investment advisors, influencers, etc. regularly forecast market performance.

the article talked about how consistently wrong these forecasts are. - how accurate are they? - not at all - why do they do this? - to get you to read - what about long term forecasts? - they are also unreliable - but better, because it's just statistical averaging. it's around 10-11 percent. Some years it's gone down, some days it goes up a lot, at the end the average will point you in a pretty reasonable direction. so bonds, the long term avg for bonds, tr like 6-7 percent.

it's never been the case that in any 20 yr period the market has gone down.

what is anchoring? - how does this apply to negotiation - for an investor, what would that look like?

Key points from last lec

  • a dollar today is worth more than a dollar tomorrow, if you buy something you like you can still get it better.

you can discount to the present time, using a discount factor, and something in the future. it's accumulated, or disaccumulated, using a discount factor. that's calculated by \(1/(1+r)^t\)

the present time atot the cash flow at time \(t\) with rate \(r\). then it's \(C_1 \times DF_1 = CF_1/(1+r)^t\)

a safe dollar is worth more than a risky dollar - the discount rate is the risk free rate plus a risk premium

the appropriate discount rate is the opportunity cost of capital - the opportunity cost is the return available on other investments of similar risks - a project has mext vale

Treasury bills, notes, bonds. This is showing you the whole spectrum of all the college benchmarks.

if we want a 2.5 yr bond, we can purchase one that is 3 years, which has a baby and dads room,

why does these change over time?

DCF is the formula to calculate total present value of these vars.

as soon as we have a non0 discount rate. if \(r\) is nonexistent, it goes to inf, if \(r\) is non zero.

sort of repayment which sets up an endow.

what is the present value of a finite sequence of \(C\) values using discount rate \(r\)?

\(\text{PV of } t\text{-year perpetuity} = C\left( \left( \frac{1}{r} \right)-\left( \frac{1}{r(1+r)^t} \right) \right)\)

this annuity is a perpetuity that starts in the past, it just puts a gap between the ramp perpetuities

we will be doing a lot of weird sequences of cash flows, etc.

suppose a perpetuity/annuity has payments that grow by a rate of \(g\)

then

\(\text{PV of growing perpetuity} = C_1/(r-g)\) if it grows faster, if \(r\) is the same as \(g\) then you have infinity.

Spreadsheets

Google sheets and excel have many built in function related to the topics we just discussed - FV is future value - PV is present value - etc.

APR and Compounding.

Vocabulary:

  • Annual Percentage Rate (APR) stated, annual rate, not accounting for compounding, dividing by apr by the # of compounding periods per year gives the return per period.
  • Effective annual rate (EAR) aka Effective APR

Given an apr of \(r\), calculate the EAR as follows.

\(EAR = (1 + r/n)^n - 1\)

is there anything that's jigng]

financial people talk in terms of basis points

\(1\text{bp} = 0.01\%\)

Key property: \(e\) is the unique base s.t. \(e^x\) grows at a rate equal to its own value as itself

to calculate the EAR, that's the formula we just saw.

we want to calculate the

BONDS

Bonds are just securities that indicate indebtedness, there's an interest rate tied to it. the person who buys the bond is lending money to the person who owns it, at a certain interest rate, for something called coupon payments. the bonds face value is returned at maturity. Visualize it like that. if you're buying a bond, money is going to go outta ur account, then you expect to receive a coupon payment semi annually.

the SEC regulates the securities market. A commodity like gold is not a security. You can buy a forward contract to buy gold in the FUTURE, a future, that's a security, but the gold itself is not a security.

there is something in between that's not really either, crypto. Bitcoin has been established by the SEC that it is not a security and will not be regulated by them.

Bonds are issued by

  • national governments
  • us treasuries
  • japanese government bonds (JGBs)
  • UK Gilts
  • French OATs
  • etc
  • government agencies
  • Fannie Mae (FNMA) - buys mortgages
  • Ginnie Mae (GNMA) - guarantees mortgages
  • municipal governments
  • to fund schools, roads, public transit
  • corporations
  • investment grade - rated BBB or above by rating agencies (Moody's etc.)
  • High Yield "Junk" - rated BB or below.

Bond Pricing

  • bonds are priced as a percentage of the face value.
  • for example a $1M bond offered at a price of:
  • 100 would cost $1M (offered at par)
  • 99.5 would cost $995,000, is said to be offered at a discount
  • 100.5 would cost $1.05M, is said to be offered at a premium

Zero Coupon Bonds

  • a 5 year, zero coupon bond, you would just get it back after 5 years.
  • these always trade at a discount
  • coupon bonds can be thought of as a portfolio of zero coupon bonds.

Internal Rate of Return

The Internal Rate of Return (IRR) is the discount rate that makes the net present value (NPV) of all cash flows associated with a project or investment equal to zero.

the discount rate has no effect on the purchase price.

you know the exact cash flows, what discount rate of cash flows would make it zero today.

  • implicitly assumes that intermediate cash flows can be reinvested at the same rate
  • usually requires numerical methods to solve
  • solution is not necessarily unique when cash flows change sign multiple times

Bonds and Yields

Yield to maturity (YTM)

  • the measure of return on investment (ROI) most commonly used in the context of bonds
  • accounts for the purchase price, coupon, and face value
  • calculated as the IRR of the bond if you hold it all the way to maturity.
  • compounding frequency matches the coupon payment frequency.
  • yields always move in the opposite direction of price.
  • so let's look at the equation.
  • if i increase the yield, if i discount into the present, then that means the value of those future payments is less, so to purchase and get the same amount i have to pay less. and vice versa.
  • bonds may be quoted using prices or yields.
  • Treasury bills, they are sold in yields over the price.
  • you should just know that if you see it

Other measures of bond yield

\(\text{Current Yield} = \text{annual coupon payment}/\text{current bond price}\)

\(\text{Nominal Yield (coupon rate)} = \text{annual coupon payment}/\text{par value}\)

Yield to call (YTC) - some bonds are callable (can be paid off early) by the issuers. - YTC is similar to YTM but assumes bond is called at earliest opportunity

Yield to worst - lowest potential yield among all possible scenarios (eg. call vs maturity)