A fear and greed index for any instrument, at any horizon

How to build a fear and greed score from 0 to 100 for Bitcoin, the S&P 500, gold or a stock, from daily or 5 minute bars, for a short, medium and long horizon.

The CNN index (US stocks) and the alternative.me index (crypto) mix several signs of fear and greed. The same method works for one instrument alone: each sign is ranked against its own history, so every component is a number from 0 to 100, and the index is their average.

Components over a horizon of h bars

Scores and index

• 0 to 25: extreme fear; 25 to 45: fear; 45 to 55: neutral; 55 to 75: greed; 75 to 100: extreme greed
• The signs that mean fear when they are high (volatility, implied volatility, put/call) enter with a minus sign
• Lookback \(L\): 365 days for daily bars, 30 days for 5 minute bars

Horizons

Short and long horizons often disagree: a short fear inside a long greed is a pullback in an up trend; a short greed inside a long fear is a rebound in a down trend. The extremes are contrarian signs: extreme fear has often come near lows, extreme greed near highs.

In R: fear_greed_get("BTC-USD", "1d") or "5m", then fear_greed_chart(); data/make_fear_greed.R saves Bitcoin, Ether, S&P 500, Nasdaq 100, gold and oil.

Estimation of the dividends of an index

The dividend yield is the one input of index futures and options that is not quoted. Three ways to estimate it, from the market view to the bottom-up count, with examples on the S&P 500, VN30 and CAC 40.

An index futures is the index carried to expiry: the buyer of the futures does not pay for the index now (interest earned) and does not receive its dividends (dividends lost). So the fair value depends on the dividends paid before expiry, which no screen quotes. With \(S\) the index, \(r\) the risk-free rate, \(q\) the dividend yield and \(T\) the time to expiry in years:

1. Implied by the futures (the market view)

It is the yield that the market prices in. It also absorbs any mispricing and the cost of funding, so it moves every day, and the futures and the index must be priced at the same moment.

2. From the total return index (the history)

\(TR\) is the total return index (dividends reinvested) and \(P\) the price index of the same basket, for example S&P 500 Total Return against S&P 500, or CAC 40 Gross Total Return against CAC 40. The difference of their 12 month returns is the dividend yield paid over the last year. The DAX is already a total return index, so its futures carry no dividend (\(q = 0\)).

3. Bottom-up from the constituents (the most accurate for short expiries)

• \(w_i\): weight of the stock in the index (free float market cap); \(D_i / P_i\): its dividend yield (announced dividend, or the last 12 months)
• \(N_i, FF_i, CAP_i\): shares, free float and cap factor used by the index; \(d_i\): cash dividend per share
• \(D_j\): dividend in index points of each ex-date \(t_j\) before expiry, in years

Examples

In VTP

The Futures tab of Pricers shows the implied dividend yield of each index futures (method 1) next to its fair value and basis, live. Type your own estimate as the dividend yield to see the fair value it gives.

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The dividend component of index futures: S&P 500 and VN30

How many index points of dividends a futures price contains, read from the futures and the index, with the December E-mini S&P 500 and the VN30F contracts.

The holder of the index receives the dividends paid before expiry; the holder of the futures does not. So the futures is below the index carried at the risk-free rate by exactly the dividends, compounded to expiry. With \(S\) the index, \(F\) the futures, \(r\) the rate and \(T\) the time to expiry in years:

The implied dividend is what the futures prices in. Compare it with the dividends you expect (announced ex-dates before expiry): if the futures implies more than you expect, it is cheap; less, it is rich.

Steps to estimate it

• Take the futures and the index at the same moment (both closes, or both intraday)
• Use the risk-free rate of the futures maturity (T-bill, interbank rate)
• Count the days to expiry: third Friday for CME index futures, third Thursday of the month for VN30F
• Compute \(PV(D) = S - F e^{-rT}\) and compare it with the sum of the announced dividends, in index points, with an ex-date before expiry

The Futures tab of Pricers computes the implied carry and dividend yield live for each index futures and for VN30F1M.

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Implied interest rates of options, by maturity

The rate to use in an option pricer can be read from the options themselves, for each expiry, with put-call parity and no model. The same fit gives the forward and the dividend yield.

For European options of the same strike and expiry, a call minus a put is a forward contract: it does not depend on volatility nor on any model.

For each expiry: take the strikes where a call and a put are both quoted, compute the mid prices \(C - P\), and fit a straight line in \(K\) (weighted by the inverse of the bid-ask spreads). The slope gives the discount factor and the rate; the intercept gives the forward. Two strikes are enough in theory: it is the box spread.

Use and limits

• Use European options (SPX, not SPY: American puts are worth more than parity says, which biases r down)
• Rates implied by options are close to the funding rates of the market makers (SOFR plus a spread), not to T-bills
• Use the rate of each expiry in the pricer and in the VIX calculation, which needs one rate per term
• In R: options_implied_rates(chain, S = 7807.24) gives one row per expiry: DAYS, R, FORWARD, Q, STRIKES, R2

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Index futures: fair value and basis

How the fair value of an index futures is computed, what the basis tells, and when to use cash and carry.

When the market futures is above its fair value it is rich: sell the futures, buy the index (cash and carry). Below, it is cheap: buy the futures, sell the index (reverse cash and carry). The gap closes at expiry, when the futures settles on the index.

Expiries: VN30F on the third Thursday of the month; CME index futures (ES, NQ, YM, RTY) on the third Friday of March, June, September and December.

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Implied volatility

The volatility that makes the model price equal to the market price of an option: what it is and how to read it.

VTP solves for \(\sigma\) by bisection between 0.1% and 500%. An implied volatility above the historical volatility means options are rich; below, cheap. Implied volatilities differ by strike (the smile or skew) and by expiry (the term structure).

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A volatility index for any underlying (VIX method)

The CBOE VIX method reads the 30 day expected volatility from out-of-the-money option prices, without a pricing model. It works for SPX, META, AAPL or any underlying with listed options.

\(Q(K)\) is the mid price of the put below \(K_0\) and of the call above it, and the average of both at \(K_0\). Going away from \(K_0\), strikes stop after two zero bids in a row. The near and next expiries around 30 days are interpolated in minutes \(N\).

Step by step

• 1. Choose the two expiries around 30 days: the last at or before 30 days (near) and the first after (next), both at least 7 days away
• 2. For each, find the strike \(K^*\) where call and put mids are closest, then the forward \(F\) and \(K_0\), the first strike at or below \(F\)
• 3. Keep the out-of-the-money puts below \(K_0\) and calls above, with a bid, until two zero bids in a row; at \(K_0\) average the put and the call
• 4. Sum the contributions \(\frac{\Delta K_i}{K_i^2} e^{RT} Q(K_i)\) and compute \(\sigma^2\) of each expiry
• 5. Interpolate the two variances to 30 days, in minutes, and take 100 times the square root

In R: vix_index(chain) for a chain, vix_yahoo(\"META\") or vix_cboe(\"SPX\") from the web, vix_day(file, date) for a saved file.

Economic policy uncertainty for Vietnam

The Baker, Bloom and Davis index counts the news articles about the economy, policy and uncertainty together. Applied to Vietnamese business news.

• An article counts when it has a term of each group: kinh tế · chính sách, thuế, NHNN... · bất định, bất ổn, rủi ro...
• Each paper is divided by its standard deviation, the papers are averaged, and the index is scaled to 100 over the base period

Category indexes (monetary, fiscal, trade, banking, property, securities) add one more group of terms. A reading of 200 means twice the usual amount of policy uncertainty in the news.