Debt and Money Markets

Summary: We can income off buying Government and Corporate Debt, which have specifications. No free lunch, only way to win is to predict the interest rate.

Introduction to Fixed Income Securities

Debt vs Equity	Debt	Equity
Payment Amount	Fixed	Variable
Payment	Fixed	Variable
Seniority	First	Last
Duration	Fixed	Perpetual
Liquidity	Low	High
Variety	Infinite	One

Geometric Mean: Multiple all numbers, then do that to the power of 1/n (nth square root)
Bond Valuation: Add all of [Coupon/(1 + YTM)^year], Coupon + Par for last payment
Rate theories: What determines interest rates?
- Market Segmentation: Each time interval determined separately
- Liquidity Premium: The longer the term the higher the rate
- Expectation: Price based off what people think future will be
Determinants of Value:
- Expected Cash Flow: Positive correlation
- Timing of Cash Flow: Sooner is better
- Discount Rate: Inverse correlation (as it is in the denominator)
If coupon > yield, premium, if coupon < yield, discount, if equal price is par
Convergence: Over time the price approaches par
Convexity: Greater percent change when discount rates decrease
Coupon: Less coupon bonds more sensitive to price
Chronological: Longer term more sensitive to price

Interest Rates

Risk Free Rate: US Treasuries
- Federal Reserve Policy
- Supply and Demand
- Exogenous (external factors)
Spread determinants: Credit risk (will it default), liquidity risk (can I sell), time to maturity
- Credit risk based off seniority and recovery rate (assets backing), rating agencies inflate, lag
4 C’s: Capacity (can they repay), Collateral (assets), Covenants (rules agreed to), Character (management)
- Capacity determined by ratios: Pros: simple, trends, audited statements. Cons: No benchmark, snapshot, past not future
- Liquidity: Short term cash.
  - Current Ratio: (current assets/current liabilities)
  - Quick ratio ((current assets-inventory)/current liabilities)
  - Net Working Capital: (current assets – current liabilities)
- Working capital: How well is firm managing inventory and trade
  - Average collection or Days Receivable: (Accounts Receivables / Sales) * 365
  - Payables Period or Days Payable: (Accounts Payable / Cost of Goods Sold) * 365
  - Inventory Holding or Conversion: (Inventory / Cost of Goods Sold) * 365
  - Cash Conversion Cycle = Days Receivable + Inventory Holding – Payables Period
- Profitability: How much money are you making: Gross profit = revenue – cost of goods sold (COGS). Net income is the amount of money a company makes after subtracting all expenses and taxes from revenue.
  - EBITDA: Earnings before interest, taxes, depreciation and amortization, Free Cash Flow
  - Margins: Gross Profit = Profit/Sales, Net Profit = Income/Sales, Operating = EBIT/Sales
  - Return on Equity = Net Income / Equity
  - Return on Assets = Net Income / Assets
- Capital Structure: Debt Ratio = Total Liabilities / Total Assets
- Coverage Ratios
  - Interest Coverage = EBIT/ Interest Expenses, MIGHT use EBITDA, DA is depreciation/amortization
- Efficiency Ratios:
  - Total Asset Turnover = Sales/Assets
  - Fixed Asset Turnover = Sales / Fixed Assets (assets that are hard to convert to cash, like a building)
- DuPont: ROE = Net Income / Equity = (Net Income/Sales) * (Sales/Assets) * (Assets/Equity)
Rate theories: What determines interest rates?
- Market Segmentation: Each time interval determined separately
- Liquidity Premium: The longer the term the higher the rate
- Expectation: Price based off what people think future will be
Calculating Spot/Forward: All the rates multiplied should be same on both sides (no arbitrage principle)

Bond Pricing

Input dates on Calculator with MM.DDYYYY format, to find change, type in first date, delta date button, second date, delta date
When in between coupons:
- NOTE: t = time passed from payment, so accrued time, T = payment period (subtract dates if act/act)
- Find PV with N, I (account for period), PMT (account for period), FV=Par
- Full Price: Find FV with N = t/T, PV=what we got above, I (account for period, same as above)
- Accrued Interest: Coupon * t/T
- Flat Price (Clean Price, what we use to compare) = Full Price – Accrued Interest
If YTM is given replace I with YTM/(P/Y)
Inverse: Yield and price are inverse, as yield represents opportunity cost, so you need to be compensated for it with price
Convexity: Decrease in rate cause greater percent increase in price, because lowering rate represents bigger delta % in rate

Callable Bonds

Callable bonds can be redeemed by the issuer at a specific time and price. This makes them cheaper, since there’s a chance they get called, which would be disadvantageous for the buyer.
To price:

Convexity

Convexity is a measure of the curvature in the price-yield relationship of a bond. It explains how duration of a bond changes as interest rates change.
Positive convexity: Bond prices rise faster when rates fall and drop slower when rates rise. Most vanilla bonds have this.
Negative convexity: The reverse—price gains are limited when rates fall. Callable bonds often exhibit this.
- Callable bonds underperform when rates fall (due to call risk).
We can use calculus to estimate.

Bonds with Embedded Options

Options: Derivatives that give option to buy or sell, zero sum (someone’s win is another’s loss)
- American (continuous), European (expiration only), Bermuda (Set times)
Callable: Issuer can buy back at specified time and price, they only will if it benefits them, always cheaper/same
- Call option more valuable at lower yields, call puts limit on bond value increases
  - Remember option free bonds have positive convexity (yield decreases have bigger impact)
Putable bonds: lets buyers sell, makes the bond more expensive
If a bond is not callable don’t use the tree, use spot rates
Binomial Tree: Up and down scenarios
- Do steps in the picture to find year two prices, then discount back to year one with same process sum all (probability * price) then add coupon.

Mortgage Backed Securities

MBS: Bundles of mortgages, securitized (able to be split) + sold to investors
- Process: Banks make loans -> Separate entity -> Entity issues -> Entity underwrites (accepts liability)
- Pros: Direct investment in mortgages, more mortgages active, cheaper rates, liquidity, bank profit
- Cons: More mortgages = more risk, hard to observe risk (since bundled)
Amortization: Gradual reduction of principal over time
Weighted Average Coupon = Sum of [(Individual Mortgage/Total Mortgage) * Rate of individual mortgage]
Weighted Average Maturity= Sum of [(Individual Mortgage/Total Mortgage) * Duration of individual mortgage]
Pass through: What the investor actually gets after bank fees
Single Monthly mortality rate: Public security association benchmark of 0.2% defaults per month, increasing by 0.2% until month 30.
Risks: Contraction (prepayments on low rates), Extension (less prepayments on high rates)
Tranches: Tiers, there’s sequential (senior paid first) and credit or default (junior takes default losses first)
Prepayment: Adds to tranche cash flow
Defaults: Does NOT add to tranche cash flow, this is lost money

Total MBS

Year	Beginning Balance	Payment	Interest	Principal	End Balance
	First one given, after that use end balance of previous column	N = Total Years I = WAC PV = BB Find PMT	BB*WAC	PMT – I	BB – Principal

Time Tranche (Junior doesn’t get paid until senior completely paid off, default risk is porportional)

Year	Beginning Balance	Interest	Principal	End Balance	Cash Flow
	First one given, after that use end balance of previous column, it’s the proportion of tranche	BB*Pass through	PMT – I	BB – Principal	Principal + Interest

Credit Tranche (Junior tranche wiped out first, the secret to doing these is to rebalance the allocation of payment following tranches disproportionally taking a default loss)

Year	Beginning Balance	Interest	Principal	End Balance	Cash Flow
	First one given, after that use end balance of previous column, it’s the proportion of tranche	BB*Pass through	PMT – I	BB – Principal	Principal + Interest