Quiz 1 – Mythical Man-Month

1. Quiz 1 – Mythical Man-Month Chapters 1-6

2. Topics for today • Review our market risk measure • Review units • Negative position amounts – shorting • Relative Pricing

3. Our “Market Risk” Measure • First order estimate – quick and dirty • Position adjusted sensitivity using 1 basis point change • Example of “bond risk”: • Price (pv): 85.731991 (that’s a total amount of $857.31 the bond is worth) • DV01: 0.092519 (how much price moves with a 1/100 of 1% change in yield = .01) • amount: 10000 (10,000 is 10MM “position”) • Position risk: 9.251928 (that’s $9,251 change to position value given a 1bp move) static double bond_risk( const SBB_bond_calculator_interface* bond_calc_ptr, const SBB_instrument_fields* bond_record_ptr, double dv_bump_amount) { double pv = bond_calc_ptr->PV(bond_record_ptr->Yield() ); double dv = bond_calc_ptr->dv_bump(bond_record_ptr->Yield(), pv, dv_bump_amount); double position_risk = bond_record_ptr->Amount() * dv/100.0; return position_risk; }

4. Getting our units right... • $10,000,000 of a bond • 9% coupon, 20 years to maturity - current price: 134.672 and yield is: 6% • Market value is: $10,000,000 * 1.346722 = $13,467,220 • Bump yield by up by 100 basis points (1%) and price is now: 121.3551 • Our data file has amounts in 000’s so $10,000,000 would be entered as 10000 • If we are short (betting against the market) the amount will be negative : -10000 • Dollar Value of an “01” (DV01) - price diff between starting yield and 1/100th of a percent move of yield, or 1 basis point, (1/100th of above example). Additionally, it is the average of two shifts: the absolute value of the differences resulting from both an up and down move. • “Risk” for us is defined as Amount * DV01/100 and thus stays in thousands since Amount is in thousands. • Risk of 44.123 means for every basis point change in yield we would gain/lose $44,123. • double yield_delta_abs = fabs(bump_amount); • // yield goes up, price goes down • double down_price = PV(base_yield + yield_delta_abs); • double price_delta_down = base_price - down_price; • // yield goes down, price goes up • double up_price = PV(base_yield - yield_delta_abs); • double price_delta_up = up_price - base_price; • dv01 = (price_delta_up + price_delta_down ) / 2.0;

5. Shorting • I think the market is going down / will “sell off” • I am contrarian • I think the price of the thing I’m interested in will drop • Borrow it from somebody • Immediately sell it to someone else • Wait for the market to drop and the price to go down • Buy it back for less money – “cover my short” • Book the difference as profit • Return it to the person I borrowed it from

6. Bond Market Rally (WSJ Quote) “U.S. government bond prices soared across the board Wednesday after the Federal Reserve’s latest policy statement boosted confidence that zero interest rate policy will stay in place for longer. The buying spree pushed down the yield on the benchmark 10-year Treasury note by the most on a one-day basis since October. The yield on the two-year note, among the most sensitive to changes in the Fed’s policy outlook, tumbled the most on a one-day basis since December 2010. Yields fall as bond prices rise.”

7. Bonds are typically priced “relative” • Generally: • Lower quality is priced relative to higher quality • Lower liquidity is priced relative to higher liquidity • Relative to what? • Individual bond • Collection of bonds (like an index) • “Spread” pricing: • Yield of Treasury = 4.68% • Yield of Corporate = 5.68% • Spread of Corporate = 100bp • Spread is measure of credit risk • Base interest rate + spread • Base interest rate + risk premium • Spread = risk premium

8. Pricing Bonds off a “Yield Curve” • Collection of liquid, high quality bonds (like an index) • Price using “spread” off matching benchmark bond • Match on maturity - the bond’s “remaining term” to “closest” benchmark • “Yield Curve” constituent criteria: • Type of Issuer • Issuer’s perceived credit worthiness • Term of maturity of the instrument • Others: optionality, taxability, expected liquidity… • The benchmark we will use is: • Current (most recently issued) “Treasuries” • “On-the-run” vs “Off-the-run” • Example: • “Trading 30 over the 10 year” • Means: “yield of the quoted bond is 30 basis points more yield than the treasury bond yield which has a maturity of 10 years” • “Treasuries” (no credit risk, highest quality, highest liquidity - benchmark to the world) • What is the “normal” shape of the “yield curve”? • How do the treasury yields come to be? • Fed funds rate, discount rate, auction results

9. Deliverables • Build a yield curve class – just another collection of bonds… • 4 bonds in curve: • 2, 5,10,30 year maturities • Load in new yield curve data file • Special version of existing “data.txt” • Bonds with ticker “T” • Load new bond data file which will include a new field: • Spread : “30bp” and tag “SPREAD” or “YIELD” • Caclulate price, dv01, risk for each bond in trading book • Example output row (will be one set of results per bond): • “SBB_0001 price dv01 risk” • Incorporating a yield curve, our “scenarios” will include shocking the yields and seeing how the trading book will change. • Typical shocks: Parallel up/down, “tilts” (flatter, steeper)