← Back to Cover
	VOLATILITY MODELING
	Historical Volatility, GARCH(1,1) Estimation & Volatility Term Structure
	HISTORICAL VOLATILITY SUMMARY
	Metric	Base	Peak	Off-Peak	Notes
	Monthly Std Dev (Log Returns)	0.2338	0.1212	0.1097	Standard deviation of monthly log returns
	Annualized Volatility	81.0%	42.0%	38.0%	Monthly vol x SQRT(12)
	Ann. Vol (from Assumptions)	35.0%	42.0%	38.0%	User-input from Assumptions sheet
	Variance (Monthly)	0.0547	0.0147	0.0120	Squared monthly standard deviation
	Mean Log Return	0.0011	0.0011	0.0011	Average monthly log return (drift)
	Downside Deviation	0.1637			Std dev of negative log returns only
	Max Monthly Loss	-0.6087			Worst single-month log return
	Max Monthly Gain	1.1291			Best single-month log return
	GARCH(1,1) VOLATILITY MODEL
	Model Parameters (from Assumptions)
	Omega (ω)	0.00005
	Alpha (α)	0.08
	Beta (β)	0.88
	α + β	0.96
	Unconditional Variance	0.00125
	Unconditional Vol (Ann.)	12.2%
	Half-life (months)	17.0
	GARCH(1,1) Conditional Variance Time Series (Base Load)
	Period	Log Return	Squared Return	Cond. Variance	Cond. Vol (Mo)	Cond. Vol (Ann)
	1	-0.0355	0.00126	0.00125	0.0354	12.2%
	2	-0.1244	0.01547	0.00125	0.0354	12.3%
	3	-0.1493	0.02228	0.00239	0.0489	16.9%
	4	-0.1524	0.02324	0.00393	0.0627	21.7%
	5	-0.0455	0.00207	0.00537	0.0733	25.4%
	6	-0.1891	0.03577	0.00494	0.0703	24.4%
	7	0.0900	0.00811	0.00726	0.0852	29.5%
	8	0.1748	0.03054	0.00709	0.0842	29.2%
	9	0.2025	0.04102	0.00873	0.0934	32.4%
	10	0.1942	0.03770	0.01101	0.1050	36.4%
	11	0.1678	0.02817	0.01276	0.1130	39.1%
	12	1.1291	1.27484	0.01353	0.1163	40.3%
	13	-0.1762	0.03105	0.11394	0.3376	116.9%
	14	-0.1236	0.01527	0.10281	0.3206	111.1%
	15	-0.1484	0.02203	0.09174	0.3029	104.9%
	16	-0.1517	0.02300	0.08254	0.2873	99.5%
	17	-0.0447	0.00200	0.07453	0.2730	94.6%
	18	-0.0496	0.00246	0.06580	0.2565	88.9%
	19	0.0881	0.00776	0.05815	0.2411	83.5%
	20	0.0340	0.00116	0.05184	0.2277	78.9%
	21	0.2033	0.04135	0.04576	0.2139	74.1%
	22	0.1950	0.03803	0.04363	0.2089	72.4%
	23	0.1686	0.02843	0.04148	0.2037	70.6%
	24	-0.6087	0.37048	0.03883	0.1971	68.3%
	25	-0.0367	0.00135	0.06386	0.2527	87.5%
	26	-0.1255	0.01575	0.05635	0.2374	82.2%
	27	-0.2892	0.08361	0.05090	0.2256	78.2%
	28	-0.1508	0.02274	0.05153	0.2270	78.6%
	29	-0.0440	0.00194	0.04722	0.2173	75.3%
	30	-0.0488	0.00238	0.04176	0.2043	70.8%
	31	0.0888	0.00788	0.03699	0.1923	66.6%
	32	0.1736	0.03013	0.03323	0.1823	63.1%
	33	0.2014	0.04057	0.03170	0.1780	61.7%
	34	0.0542	0.00293	0.03119	0.1766	61.2%
	35	0.1694	0.02871	0.02773	0.1665	57.7%
	36	-0.5249	0.27555	0.02675	0.1636	56.7%
	37	-0.0359	0.00129	0.04564	0.2136	74.0%
	38	-0.1248	0.01557	0.04031	0.2008	69.6%
	39	-0.1497	0.02241	0.03677	0.1918	66.4%
	40	-0.1528	0.02335	0.03420	0.1849	64.1%
	41	-0.1846	0.03409	0.03202	0.1789	62.0%
	42	-0.0479	0.00229	0.03095	0.1759	60.9%
	43	0.0895	0.00802	0.02747	0.1657	57.4%
	44	0.1744	0.03040	0.02486	0.1577	54.6%
	45	0.2020	0.04082	0.02436	0.1561	54.1%
	46	0.1939	0.03758	0.02476	0.1573	54.5%
	47	0.1675	0.02806	0.02484	0.1576	54.6%
	48	-0.3198	0.10226	0.02415	0.1554	53.8%
	49	-0.0352	0.00124	0.02949	0.1717	59.5%
	50	-0.1238	0.01532	0.02610	0.1615	56.0%
	51	-0.1490	0.02220	0.02424	0.1557	53.9%
	52	-0.1520	0.02310	0.02316	0.1522	52.7%
	53	-0.0452	0.00204	0.02228	0.1493	51.7%
	54	-0.0498	0.00248	0.01982	0.1408	48.8%
	55	-0.0513	0.00263	0.01769	0.1330	46.1%
	56	0.1752	0.03070	0.01583	0.1258	43.6%
	57	0.2029	0.04116	0.01643	0.1282	44.4%
	58	0.1946	0.03787	0.01780	0.1334	46.2%
	59	0.1682	0.02829	0.01875	0.1369	47.4%
	GARCH Summary Statistics
	Average Cond. Vol (Ann.)	59.3%
	Max Cond. Vol (Ann.)	116.9%
	Min Cond. Vol (Ann.)	12.2%
	Latest Cond. Vol (Ann.)	47.4%
	VOLATILITY TERM STRUCTURE (Forward-Looking)
	Tenor (Months)	GARCH Forecast	Flat Vol	Blend	Decay Factor
	1	46.5%	35.0%	46.5%	100.0%
	2	45.7%	35.0%	44.7%	90.9%
	3	44.8%	35.0%	43.0%	81.8%
	4	44.0%	35.0%	41.5%	72.7%
	5	43.2%	35.0%	40.2%	63.6%
	6	42.3%	35.0%	39.0%	54.5%
	7	41.6%	35.0%	38.0%	45.5%
	8	40.8%	35.0%	37.1%	36.4%
	9	40.1%	35.0%	36.4%	27.3%
	10	39.3%	35.0%	35.8%	18.2%
	11	38.6%	35.0%	35.3%	9.1%
	12	37.9%	35.0%	35.0%	0.0%
	Note: GARCH parameters are from Assumptions sheet. Conditional variance is computed recursively. Term structure blends GARCH forecast with flat historical vol for longer tenors.