Funding arbitrage, basis with futures and cross-exchange arbitrage.

Three ways to collect the carry

Lesson 2.3.7 introduced the cash-and-carry: buy the coin spot and sell the same quantity in a derivative, so that the price does not matter and the carry remains. With the level 3 data it can be done with four exchanges and two assets, with perpetuals and with quarterlies, and measure what lesson 2.3.7 only listed: how much margin the short leg needs, when it is liquidated, when the future pays off and what happens when the exchange goes bankrupt. There are three variants:

flowchart TB
  C[Long spot] --> P[Short perpetual]
  C --> T[Short quarterly]
  C --> O[Perp. other exch.]
  P --> F[Variable funding]
  T --> B[Locked-in basis]
  O --> R[Two counterparties]

• With the perpetual. It collects each period's funding, which changes and can turn negative.
• With the quarterly. The basis is locked in at opening: at expiry the future settles to the index and the result is the initial difference, whatever funding does.
• Split across exchanges. The spot on one and the derivative on another, or the derivative on the one that pays the most. It gains some carry or margin and adds a counterparty.

import numpy as np
import pandas as pd

fu = pd.read_parquet("cripto3_funding.parquet")
carry = (100 * fu.groupby(["activo", "exchange",
                           fu["ts"].dt.year])["tasa_funding"]
         .sum()).unstack()
print("funding collected by the short, % of notional per year:")
print(carry.round(1).to_string())
suelo = 100 * 0.0001 * 3 * 365
print(f"floor of the interest term: {suelo:.2f}% a year")

funding collected by the short, % of notional per year:
ts               2020  2021  2022  2023  2024  2025
activo exchange
XBQ    alfa      25.6  24.4  10.4  11.8  11.2   9.7
       boreal    28.7  26.4  11.4  13.3  12.2  10.5
       cenit     23.7  23.0   8.8  10.8   9.9   8.8
       dedalo    29.8  28.7   7.5   NaN   NaN   NaN
XEQ    alfa      52.9  38.3  11.7  12.4  10.9   9.4
       boreal    55.5  40.0  13.4  13.8  11.9  10.4
       cenit     49.9  35.6   9.6  11.8  10.2   8.6
       dedalo    59.5  42.8  10.1   NaN   NaN   NaN
floor of the interest term: 10.95% a year

The table is what the perpetual's short collected each year, in % of notional, without costs or compounding. For XBQ, from 23.0% to 29.8% in 2020 and 2021 depending on the exchange; since 2022, between 8.8% and 13.3% on the three that survive. XEQ pays double in the years of euphoria (from 49.9% to 59.5% in 2020) and almost the same as XBQ afterwards. The figure at the top draws the XBQ lines. Two things stand out: dedalo is the one that pays the most while it exists, and since 2022 all the others stick to the 10.95% floor set by the formula's interest term ($0.01\,\% \times 3 \times 365$, lesson 3.7.1).

That floor deserves attention. It is not the dollar interest rate or the result of supply and demand: it is a constant of the exchange's formula, the one a long pays while the premium is inside the band. The “market” carry is what lies above it, and in the data it is planted as a bullish premium that narrows with a half-life of 2.5 years (more capital devoted to arbitraging it). Is that half-life recovered?

from scipy.optimize import curve_fit

a = fu[(fu["exchange"] == "alfa") & (fu["activo"] == "XBQ")]
a = a.set_index("ts")
r7 = np.log(a["precio_indice"] / a["precio_indice"].shift(21))
z = np.tanh(r7 / 0.15)                   # euphoria: z close to 1
d = pd.DataFrame({"prima": a["prima_media"], "z": z}).dropna()
d["anos"] = (d.index - d.index[0]).days / 365.25
eu = d[d["z"] > 0.5]


def prima_alcista(X, amp, vida):
    anos, z = X
    return amp * np.exp(-np.log(2) * anos / vida) * z ** 2


(amp, vida), _ = curve_fit(prima_alcista, (eu["anos"], eu["z"]),
                           eu["prima"], p0=[0.003, 2.0])
print(f"{len(eu)} euphoria periods; amplitude {1e4 * amp:.1f} bp,"
      f" half-life {vida:.2f} years")
print((1e4 * eu["prima"] / eu["z"] ** 2).groupby(eu.index.year)
      .mean().round(1).to_dict())

1091 euphoria periods; amplitude 33.7 bp, half-life 2.53 years
{2020: 29.0, 2021: 23.1, 2022: 15.8, 2023: 14.2, 2024: 10.0, 2025: 7.2}

In the 1,091 periods of euphoria (high 7-day return, $\tanh(r_7/0.15) > 0.5$), a nonlinear fit recovers an amplitude of 33.7 basis points per period and a half-life of 2.53 years, versus the planted 35 and 2.5. The premium per unit of euphoria falls from 29.0 basis points in 2020 to 7.2 in 2025. The data is not reality, but the direction matches what He, Manela, Ross and von Wachter document: the deviations of perpetuals from their no-arbitrage price have been shrinking over time11Note 1 · S. He, A. Manela, O. Ross and V. von Wachter, “Fundamentals of Perpetual Futures”, arXiv 2212.06888 (version 1 from December 2022, revised later). The abstract says the deviations are larger than in currency markets, comove across coins and shrink over time; the lesson does not cite figures from the paper..

The short leg needs margin

The cash-and-carry has no price risk on paper, but the capital is not just the spot. The short leg needs margin, and with isolated margin it is liquidated if the mark rises to its liquidation price, even if the spot has gained the same (lesson 3.7.1). With leverage $L$ on that leg, the capital per unit of notional is $1 + 1/L$ and the return on capital, the carry divided by that amount. More leverage raises the return and brings liquidation closer. The 1-hour bars of alfa let us count how many times it would have happened if every week (or every month) the margin were topped up and the short leg reopened at the price of that moment:

h1 = pd.read_parquet("cripto3_1h.parquet")
b = h1[h1["activo"] == "XBQ"].set_index("ts")
f_alfa = a["tasa_funding"]
anual = f_alfa.sum() / ((f_alfa.index[-1] - f_alfa.index[0]).days
                        / 365.25)
MMR = 0.005
filas = []
for L in (1, 2, 3, 5, 10, 20):
    fila = {"apal_corto": L,
            "rend_capital_pct": 100 * anual / (1 + 1 / L)}
    for nombre, frec in (("semanal", "7D"), ("mensual", "30D")):
        g = b.groupby(pd.Grouper(freq=frec))
        liq = g["apertura"].first() * (1 + 1 / L) / (1 + MMR)
        fila[f"liq_{nombre}"] = int((g["mark_maximo"].max() >= liq)
                                    .sum())
    filas.append(fila)
print(f"average carry on alfa, XBQ: {100 * anual:.1f}% of notional")
pd.DataFrame(filas).set_index("apal_corto").round(1)

average carry on alfa, XBQ: 15.5% of notional
            rend_capital_pct  liq_semanal  liq_mensual
apal_corto
1                        7.8            0            0
2                       10.4            0            2
3                       11.6            1            9
5                       12.9            8           28
10                      14.1           71           52
20                      14.8          180           60

The average carry of XBQ on alfa is 15.5% a year of notional. Without leverage on the short (1x), the capital doubles and the return falls to 7.8%; with 3x, 11.6%, and in six years the mark would have liquidated the short in only one week; with 10x, 14.1%, but 71 weeks out of 314 end with the short liquidated and the spot unhedged. With monthly rebalancing the risk grows at low leverage (9 liquidations at 3x versus 1): in 30 days the price has more time to rise before the margin is topped up. The monthly figures at 10x and 20x are lower only because there are fewer months than weeks. The chart sums up the trade-off: the last points of return are paid for with a number of liquidations that grows much faster.

Costs count too. Entering and exiting pays four sides (buying and selling spot, selling and buying back the perpetual). With an assumption of 5 basis points per side, on the order of the commission of a client taking liquidity on a large exchange (lesson 2.4.7), it costs:

COMISION = 5 / 1e4          # assumption: 5 bp per side and leg
lados = 4                   # buy and sell spot and perpetual
for nombre, diario in [("floor (0.03% daily)", 0.0003),
                       ("2025 average", carry.loc[("XBQ", "alfa"),
                                                  2025] / 100 / 365)]:
    dias = lados * COMISION / diario
    print(f"{nombre}: {dias:.1f} days of carry to pay for entry"
          " and exit")

floor (0.03% daily): 6.7 days of carry to pay for entry and exit
2025 average: 7.5 days of carry to pay for entry and exit

About 7 days of carry at the floor, 7.5 at the 2025 pace. A cash-and-carry that is opened and closed often, for example every time a week's funding drops (exercise of lesson 2.3.7), eats the carry in commissions.

The basis of the quarterlies

cripto3_futuros.parquet has a daily snapshot, at 00:00 UTC, of the two nearest quarterlies of each exchange and asset; they expire on the last Friday of March, June, September and December at 08:00 UTC. The annualized basis is measured with the index at the same time, as $\ln(F/S) \times 365/\text{days}$:

ft = pd.read_parquet("cripto3_futuros.parquet")
ind = (fu[fu["exchange"] == "alfa"]
       .set_index(["ts", "activo"])["precio_indice"])
ft = ft.join(ind, on=["ts", "activo"]).dropna(subset=["precio_indice"])
ft["basis"] = np.log(ft["precio"] / ft["precio_indice"]) * 365 \
    / ft["dias"]
vivos = ft[ft["exchange"] != "dedalo"]
err = 100 * (vivos["basis"] - vivos["basis_anual_modelo"]).abs()
print(f"error versus the model's (points): median {err.median():.4f}"
      f", maximum {err.max():.2f}, maximum beyond 10 days "
      f"{err[vivos['dias'] > 10].max():.2f}")
x = vivos[(vivos["exchange"] == "alfa") & (vivos["activo"] == "XBQ")]
orden = x.groupby("ts").cumcount()
primero, segundo = x[orden == 0], x[orden == 1]
print("average basis of the front quarterly, % a year:")
print((100 * primero.groupby(primero["ts"].dt.year)["basis"].mean())
      .round(1).to_dict())
dif = (segundo.set_index("ts")["basis"] - primero.set_index("ts")
       ["basis"])
print(f"second minus first: {100 * dif.mean():+.2f} points")

error versus the model's (points): median 0.0029, maximum 1.33, maximum beyond 10 days 0.26
average basis of the front quarterly, % a year:
{2020: 22.3, 2021: 23.1, 2022: 10.9, 2023: 11.9, 2024: 11.1, 2025: 9.2}
second minus first: +0.40 points

The measured basis matches the model column with a median of 0.003 points; the maximum error, 1.33 annualized points, appears in the last days before expiry, when the rounding of the price to the tick is multiplied by 365 divided by a few days (beyond 10 days, 0.26). The average basis of the front XBQ quarterly on alfa is 22.3% and 23.1% in 2020 and 2021, and from 9.2% to 11.9% afterwards, in line with funding. The second quarterly trades 0.40 annualized points above the first: the planted term premium.

The practical question is whether it pays to lock in the basis or collect the funding. For each quarterly, the cash-and-carry is opened when it has about 95 days left and the locked-in basis (in % of notional for the whole quarter) is compared with the funding the perpetual would have collected from that day until expiry:

def trimestres(fut, fund):
    """Per contract: basis locked in at <= 95 days to expiry, funding
    collected until expiry and that of the previous 90 days (%)."""
    filas = []
    for contrato, c in fut.groupby("contrato"):
        ent = c[c["dias"] <= 95].head(1)
        if ent.empty:
            continue
        e0 = ent.iloc[0]
        t0 = e0["ts"]
        vto = (pd.Timestamp(e0["vencimiento"]).tz_localize("UTC")
               + pd.Timedelta(hours=8))
        if t0 < pd.Timestamp("2020-02-01", tz="UTC") or vto.year > 2025:
            continue
        hasta_vto = fund[(fund.index > t0) & (fund.index <= vto)].sum()
        previo = fund[(fund.index > t0 - pd.Timedelta(days=90))
                      & (fund.index <= t0)].sum()
        filas.append({"contrato": contrato,
                      "fijado": 100 * np.log(e0["precio"]
                                             / e0["precio_indice"]),
                      "funding": 100 * hasta_vto,
                      "funding_previo": 100 * previo})
    return pd.DataFrame(filas).set_index("contrato")


q = trimestres(x, f_alfa)
print(q.round(2).head(8).to_string())
print(f"{len(q)} quarters; locked-in mean {q['fijado'].mean():.2f}%,"
      f" funding collected {q['funding'].mean():.2f}%, correlation "
      f"{q['fijado'].corr(q['funding']):.2f}")
elige = np.where(q["fijado"] > q["funding_previo"], q["fijado"],
                 q["funding"])
print(f"rule “the larger of the two at opening”: {elige.mean():.2f}% "
      f"per quarter")

            fijado  funding  funding_previo
contrato
XBQ-200626    2.04     8.94            2.81
XBQ-200925    2.15     4.49            8.81
XBQ-201225    1.23     8.87            4.37
XBQ-210326   11.98    14.12            8.52
XBQ-210625    1.00     3.76           13.68
XBQ-210924    2.51     4.05            3.73
XBQ-211231   15.55     2.90            4.75
XBQ-220325    3.58     2.27            4.19
23 quarters; locked-in mean 3.97%, funding collected 3.97%, correlation 0.24
rule “the larger of the two at opening”: 5.14% per quarter

Over 23 quarters, the mean of the locked-in basis is 3.97% per quarter and that of the funding collected, also 3.97%. Locking in neither wins nor loses on average: it removes uncertainty. The correlation between the two is only 0.24, and the figure shows why: in any given quarter one beats the other by several points. The quarterly expiring in December 2021 locked in 15.55% and that quarter's funding gave 2.90%; the one expiring in June 2020 locked in 2.04% while funding gave 8.94%.

Since the basis in the data carries noise of its own that does not anticipate the next funding, a rule without information from the future exploits it: lock in the basis if it is larger than the funding of the previous 90 days and, if not, stay with the perpetual. It gives 5.14% per quarter. It is exercise 3; before believing it in real markets one would need to check whether, there, the noise of the basis is independent of future funding, and with 23 observations per pair the standard error is large.

Between exchanges: funding differentials and dislocations

Each exchange computes its funding with its own premium. If one systematically pays more than another, one can be short the perpetual of the one that pays more and long that of the one that pays less, without spot: the funding differential.

p = fu[fu["activo"] == "XBQ"].pivot(index="ts", columns="exchange",
                                     values="tasa_funding")
dif = 100 * p.sub(p["alfa"], axis=0).drop(columns="alfa")
print("difference with alfa, percentage points per year:")
print(dif.groupby(dif.index.year).sum(min_count=1).round(2).T
      .to_string())
diferencial = p["boreal"] - p["cenit"]
print(f"periods in which boreal pays the same as cenit: "
      f"{100 * (diferencial.abs() < 1e-9).mean():.1f}%")

difference with alfa, percentage points per year:
ts        2020  2021  2022  2023  2024  2025
exchange
boreal    3.03  1.99  1.05  1.42  0.98  0.86
cenit    -1.93 -1.44 -1.59 -1.05 -1.32 -0.87
dedalo    4.19  4.33 -1.72   NaN   NaN   NaN
periods in which boreal pays the same as cenit: 71.4%

boreal pays 3.03 points a year more than alfa in 2020 and 0.86 in 2025; cenit, between 0.87 and 1.93 less every year; dedalo, 4.19 and 4.33 more in 2020 and 2021. The planted premium of each exchange is constant (half a basis point more on boreal, half less on cenit), but the differential narrows every year. The reason is the formula's band: in 71.4% of the periods boreal and cenit pay exactly the same, the fixed basis point. The difference in premiums only passes into funding when the premium leaves the band, in the weeks of euphoria, and those are less and less profitable. Exercise 2 computes what is left after costs.

Dislocations are something else: an exchange's spot price separates from the others' for a few hours. There are four planted in the data; the published daily closes reveal two:

cd = pd.read_parquet("cripto3_diario.parquet")
xb = cd[cd["activo"] == "XBQ"]
sp = xb.pivot(index="fecha", columns="exchange", values="cierre_spot")
ok = xb.pivot(index="fecha", columns="exchange",
              values="retiradas_abiertas")
indice = sp.where(ok == True).median(axis=1)
desv = 100 * np.log(sp.div(indice, axis=0))
for e in ["alfa", "boreal", "cenit"]:
    m = desv[e].abs()
    print(f"{e}: standard deviation {desv[e].std():.3f}%, worst day "
          f"{m.idxmax():%Y-%m-%d} ({desv[e][m.idxmax()]:+.2f}%)")

alfa: standard deviation 0.092%, worst day 2025-10-10 (-3.96%)
boreal: standard deviation 0.035%, worst day 2020-01-23 (+0.14%)
cenit: standard deviation 0.122%, worst day 2020-03-12 (-5.45%)

Outside those days, each exchange's spot deviates from the index with a standard deviation of between 0.035% and 0.122%, less than any commission. The two large episodes are that of March 12, 2020 on cenit (−5.45%) and that of October 10, 2025 on alfa (−3.96%), both in the middle of a sell-off. Exploiting them requires buying on the cheap exchange and selling on the others at the same time, which can only be done with inventory already in place at both venues: there is no time to move coins or dollars from one exchange to another while it lasts. And they happen when order books are thinnest, withdrawals most congested and the risk that the cheap exchange has a real problem is highest. A dislocation can be an opportunity or the first symptom of a bankruptcy.

Counterparty risk: the bankruptcy of dedalo

dedalo was, until November 2022, the exchange that paid best. The timeline of its bankruptcy is in cripto3_exchanges.csv and is inspired by that of FTX, without copying it:

stateDiagram-v2
  [*] --> Normal
  Normal --> Rumors: Nov 6
  Rumors --> Suspension: Nov 8 12:00
  Suspension --> Halt: Nov 11 14:00
  Halt --> Bankruptcy: Nov 11 23:00
  Bankruptcy --> [*]

With the suspension, withdrawals are closed and balances stop being convertible; the dedalo spot trades at a growing discount and drops out of the index; funding turns very negative; at 14:00 on the 11th trading halts and, for the course, balances and positions are worth zero.

ded = (fu[(fu["exchange"] == "dedalo") & (fu["activo"] == "XBQ")]
       .set_index("ts"))
hasta = pd.Timestamp("2022-11-08 08:00", tz="UTC")
c_ded = ded["tasa_funding"][:hasta].sum()
c_alfa = f_alfa[:hasta].sum()
anos = (hasta - ded.index[0]).days / 365.25
print(f"cumulative carry until {hasta:%Y-%m-%d}: dedalo "
      f"{100 * c_ded:.1f}%, alfa {100 * c_alfa:.1f}% of notional")
print(f"dedalo premium: {100 * (c_ded - c_alfa) / anos:.2f} points"
      " a year")
ded[ded.index >= "2022-11-08"][["precio_indice", "ultimo",
                                "tasa_funding"]].head(7)

cumulative carry until 2022-11-08: dedalo 69.3%, alfa 59.2% of notional
dedalo premium: 3.53 points a year
                           precio_indice   ultimo  tasa_funding
ts
2022-11-08 00:00:00+00:00        22086.5  22098.6      0.000100
2022-11-08 08:00:00+00:00        22055.8  22068.4      0.000100
2022-11-08 16:00:00+00:00        20037.7  20012.2     -0.002016
2022-11-09 00:00:00+00:00        19958.3  19190.9     -0.003800
2022-11-09 08:00:00+00:00        19623.3  18367.6     -0.002295
2022-11-09 16:00:00+00:00        21563.9  20084.3     -0.004368
2022-11-10 00:00:00+00:00        19746.2  17699.2     -0.003066

Until November 8, 2022, the short of the XBQ perpetual collected 69.3% of notional on dedalo and 59.2% on alfa: a premium of 3.53 points a year for being on dedalo. The table shows how it ends. On the 8th at 16:00, four hours after withdrawals were suspended, the dedalo perpetual already trades slightly below the index and funding is −0.20% per period: now the shorts pay. The next day the discount is 3.8% and funding, −0.38%.

The figure follows the whole episode: the dedalo perpetual glued to the index until the suspension and a discount that reaches 17% on the 11th; funding, from one basis point before to between −20 and −50 basis points per period after, with one period at the −50 basis point cap. Nothing in the prices or the funding of the previous days gave a warning. What is left of a cash-and-carry depending on how the capital had been allocated?

L = 3
capital = 1 + 1 / L            # per unit of notional: spot + margin
retirado = ded["tasa_funding"][:"2022-10-31"].sum()  # at month end
c = {e: fu[(fu["exchange"] == e) & (fu["activo"] == "XBQ")]
     .set_index("ts")["tasa_funding"][:hasta].sum()
     for e in ["alfa", "boreal", "cenit"]}
escenarios = {
    "all on dedalo, no withdrawals": 0.0,
    "all on dedalo, withdrawing every month": retirado,
    "a quarter on each exchange": (3 * capital + sum(c.values())
                                   + retirado) / 4,
    "all on alfa": capital + c["alfa"],
}
for k, v in escenarios.items():
    print(f"{k:40s} {v / capital:6.2f} times the capital")
riesgo = (c_ded - c_alfa) / anos / capital
print(f"dedalo premium on capital: {100 * riesgo:.1f}% a year")

all on dedalo, no withdrawals              0.00 times the capital
all on dedalo, withdrawing every month     0.52 times the capital
a quarter on each exchange                 1.22 times the capital
all on alfa                                1.44 times the capital
dedalo premium on capital: 2.6% a year

The four figures are the final capital, as of November 11, 2022, per unit of initial capital, with the short at 3x and without costs. With everything on dedalo and without withdrawing profits, zero: the spot, the margin and almost three years of carry. If the carry was withdrawn at the end of each month, 0.52 remains, the carry taken out; the capital is lost. Split equally across the four exchanges, 1.22: the quarter on dedalo is lost and the rest collects. Everything on alfa, 1.44. The dedalo premium, 3.53 points of notional a year, is 2.6% a year of capital: it is the annual probability of bankruptcy that the premium compensated if a bankruptcy destroys the capital deposited. Nobody could estimate it from prices.

For a carry strategy, the lesson is direct. The exchange is not neutral infrastructure: it is the counterparty of everything deposited on it. Higher funding or basis on an exchange can be the signal that the market is asking it for a premium for that risk. The defenses are those of any credit risk: limits per counterparty, periodic withdrawal of profits, separate custody when the exchange offers it and exchanges with verifiable supervision and asset segregation (lesson 3.7.5 covers the European framework).

What this changes in a carry backtest

• Carry net of the floor. Separate the 10.95% set by the formula from the market premium: the latter is the one that narrows, and the one a strategy tries to capture.
• Margin and liquidations of the short leg. Simulate the margin with the intraday mark and a realistic top-up frequency; a cash-and-carry without margin is not the strategy that can be traded.
• Costs per switch. Four sides each time you enter and exit: a week of carry.
• Lock in or float. The quarterly removes funding uncertainty until expiry, but it has its own rolls and its own margin.
• One counterparty per exchange. A backtest with prices from an exchange that no longer exists includes its carry and not its bankruptcy if the universe is built with the exchanges still alive: it is survivorship bias (lesson 2.5.1).

Exercises

1. Repeat the short-leg leverage table for XEQ on alfa (2x, 3x and 5x, weekly rebalancing). What changes and why?

bq = h1[h1["activo"] == "XEQ"].set_index("ts")
fe = fu[(fu["exchange"] == "alfa") & (fu["activo"] == "XEQ")]
fe = fe.set_index("ts")["tasa_funding"]
anual_e = fe.sum() / ((fe.index[-1] - fe.index[0]).days / 365.25)
filas = []
for L in (2, 3, 5):
    g = bq.groupby(pd.Grouper(freq="7D"))
    liq = g["apertura"].first() * (1 + 1 / L) / (1 + MMR)
    filas.append({"apal_corto": L,
                  "rend_capital_pct": 100 * anual_e / (1 + 1 / L),
                  "liq_semanal": int((g["mark_maximo"].max() >= liq)
                                     .sum())})
pd.DataFrame(filas).set_index("apal_corto").round(1)

            rend_capital_pct  liq_semanal
apal_corto
2                       15.1            0
3                       17.0            5
5                       18.9           25

2. Compute the annual result of a funding differential long the cenit perpetual and short the boreal one (XBQ, same notional), deducting one entry and one exit per year at 5 basis points per side. Is it worth the capital and the two counterparties?

neto = diferencial.groupby(diferencial.index.year).sum() * 100
neto = neto - 4 * 5 / 1e4 * 100    # enter and exit once a year
neto.round(2).to_dict()

{2020: 4.76, 2021: 3.24, 2022: 2.44, 2023: 2.28, 2024: 2.1, 2025: 1.53}

3. Apply the rule “lock in the basis if it is larger than the funding of the previous 90 days” to the six exchange and asset pairs that survive. Does it always beat the perpetual alone? What would make you distrust the result on real data?

filas = []
for (e, ac), fut in ft[ft["exchange"] != "dedalo"].groupby(
        ["exchange", "activo"]):
    fund = (fu[(fu["exchange"] == e) & (fu["activo"] == ac)]
            .set_index("ts")["tasa_funding"])
    q2 = trimestres(fut, fund)
    fija = q2["fijado"] > q2["funding_previo"]
    filas.append({"exchange": e, "activo": ac,
                  "fijado": q2["fijado"].mean(),
                  "perpetuo": q2["funding"].mean(),
                  "regla": np.where(fija, q2["fijado"],
                                    q2["funding"]).mean(),
                  "fija_pct": 100 * fija.mean()})
pd.DataFrame(filas).set_index(["exchange", "activo"]).round(2)

                 fijado  perpetuo  regla  fija_pct
exchange activo
alfa     XBQ       3.97      3.97   5.14     43.48
         XEQ       3.92      5.30   6.55     43.48
boreal   XBQ       4.44      4.38   5.33     52.17
         XEQ       4.18      5.69   7.04     21.74
cenit    XBQ       3.13      3.62   4.42     26.09
         XEQ       3.58      4.88   6.26     21.74