PATH/INTERMEDIATE/fixed-income-essentials/3 STOPS · 1.3 hr

Fixed Income Essentials

Bond Math, Duration, and Yield-Curve Risk

Bond pricing, yield to maturity, modified duration, convexity — and how to use them to size interest-rate risk. The practitioner pieces that come up daily on a rates desk.

Treasurers, fixed-income analysts, FRM Part I candidates.

By the end you will…

Price any bond by discounting cash flows and back out yield to maturity.

Compute modified duration and convexity to size interest-rate risk.

Compare credit risk via spread-to-Treasury frameworks.

Slot fixed income into a strategic asset allocation that matches a risk profile.

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01 / THE JOURNEY

The journey

3 STOPS · 1.3 hr · INTERMEDIATE

STOP 1 · 35 MIN · Valuation

● You are here

Bond Pricing & YTM

DCF bond pricing, yield to maturity, duration, convexity. With live curves.

DCF bond pricing, YTM, modified duration, convexity — all in one.

Open lab →

Worked example

10-year, 4% coupon, $1000 face, semi-annual — bond price vs YTM.

YTM	Price	Δ from par
3.0%	$1,085.30	+8.53%
4.0%	$1,000.00	0.00%
5.0%	$ 922.05	−7.80%
6.0%	$ 850.61	−14.94%

STOP 2 · 20 MIN · Risk & Return

Risk & Return Statistics

Compute E(r), σ², σ, Sharpe, skew, kurtosis from probabilistic or historical data.

Apply the same risk/return framework to a bond return series.

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Worked example

Annual returns: AGG (US Aggregate Bond) vs SPY (last 10y).

Series	Mean	σ	Sharpe	Max DD
AGG (bonds)	2.4%	5.8%	0.07	−16.3%
SPY (stocks)	12.5%	16.2%	0.53	−33.7%

STOP 3 · 25 MIN · Portfolio Construction

Asset Allocation Wizard

Risk profile questionnaire then recommended allocation plus 10y backtest.

Slot bonds into a strategic allocation matched to your risk profile.

Open lab →

Worked example

Conservative profile: 70% bonds. Backtested 10y on AGG + GLD + SPY.

Profile	Bonds	Stocks	Alts	10y CAGR	Max DD
Conservative	70%	20%	10%	+5.1%	−9.2%
Moderate	35%	50%	15%	+8.4%	−18.5%
Aggressive	15%	70%	15%	+11.2%	−27.8%

02 / CASE STUDIES

Apply what you learned

2 SCENARIOS

Case Study

Should I buy a 10-year Treasury at 4% or a corporate at 6%?

The 'extra 2% yield' isn't free — it's the price of credit risk. A BBB-rated 10y corporate at 6% trades at a 200 bp spread to the 4% Treasury. Historical default rates on BBB over 10 years are ~3.5% cumulative; assume 40% recovery, so expected loss ≈ 2.1%. The 'real' risk-adjusted yield on the corporate is closer to 4%, basically matching the Treasury. Plus the corporate carries 8.1 years of modified duration vs Treasury's 8.5y — a 100bp rate move costs you 8% either way. Run the numbers in Bond Pricing → toggle YTM and compare prices side by side. Lesson: spread compensates for default risk, not for free yield.

Try the Bond Pricing & YTM →Try the Risk & Return Statistics →

Case Study

Indonesian SBN vs US T-Bond for an Indonesian retiree

10y Indonesian SBN (FR-series government bond) yields ~6.7%. 10y US Treasury yields ~4.0%. Local advantage: SBN pays in IDR with no FX risk to a domestic spender. But IDR has depreciated ~3% annualized against USD over 20 years, and Indonesian inflation runs ~3-4% vs US 2-2.5%. Real yield on SBN: ~3.0%. Real yield on UST (USD): ~1.7% — but for an Indonesian who needs to spend in IDR, USD-denominated bonds add 50-200 bps of FX volatility (σ ~10% on USD/IDR). The Bond Pricing Lab handles both curves; the Asset Allocation Wizard's Indonesia mode lets you mix them with a duration target.

Try the Bond Pricing & YTM →Try the Asset Allocation Wizard →

Free for any classroom or self-study use. Each Lab works standalone too — this path is one suggested ordering of the foundations.

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Fixed Income Essentials

Bond Math, Duration, and Yield-Curve Risk

Bond pricing, yield to maturity, modified duration, convexity — and how to use them to size interest-rate risk. The practitioner pieces that come up daily on a rates desk.

Treasurers, fixed-income analysts, FRM Part I candidates.

By the end you will…

Price any bond by discounting cash flows and back out yield to maturity.

Compute modified duration and convexity to size interest-rate risk.

Compare credit risk via spread-to-Treasury frameworks.

Slot fixed income into a strategic asset allocation that matches a risk profile.

YTM

Price

Δ from par

3.0%

$1,085.30

+8.53%

4.0%

$1,000.00

0.00%

5.0%

$ 922.05

−7.80%

6.0%

$ 850.61

−14.94%

Series

Mean

Sharpe

Max DD

AGG (bonds)

2.4%

5.8%

0.07

−16.3%

SPY (stocks)

12.5%

16.2%

0.53

−33.7%

Profile

Bonds

Stocks

Alts

10y CAGR

Max DD

Conservative

70%

20%

10%

+5.1%

−9.2%

Moderate

35%

50%

15%

+8.4%

−18.5%

Aggressive

15%

70%

15%

+11.2%

−27.8%