Intraday covariance halves daily-rebalanced Borsa Istanbul MVP turnover

Feeding intraday covariance into a daily-rebalanced minimum-variance optimizer halves the trading bill on Borsa Istanbul with barely any change in risk. In Taş's three-month-window comparison, annualized volatility was 26.68% for the portfolio using 30-minute realized covariance and 26.71% for the daily-covariance portfolio. Average gross turnover per rebalance was 2.39% against 5.37%. Those are the figures a desk should remember. The headline Sharpe ratios carry less weight. Taş raises turnover in his abstract, though he confines the claim to the three-month window. Tables 2 and 3 support a wider claim: turnover falls at all four windows under both rebalancing frequencies.

Building the portfolios

Taş starts with Matriks adjusted 5-minute data for 11 stocks. Each trading day, he calculates log returns over 5-minute or 30-minute bars. He sums the outer products of those intraday return vectors, then adds the outer product of the overnight return. This produces a full-day realized covariance matrix in the Hansen-Lunde style. He averages the daily matrices over rolling windows of 1, 3, 6 or 12 months and feeds the result into a long-only global minimum-variance optimizer. The portfolio is fully invested, with a 20% cap per stock. These are the paper's HF-MVP 5m and HF-MVP 30m portfolios. Daily-MVP solves the same problem, using covariance estimated from averaged outer products of daily close-to-close returns over the matching window.

The statistical case is straightforward. Many observations within a day estimate covariance more tightly than a single close-to-close return. As the window advances, the estimate should shift less. Steadier estimates produce steadier weights and less trading.

The universe contains the 11 names that belonged to BIST 30 at the start of 2017 and had continuous 5-minute data through 2025: AKBNK, ASELS, BIMAS, EREGL, GARAN, ISCTR, KCHOL, SAHOL, TCELL, THYAO and TUPRS. Estimates are initialized with 2017. The out-of-sample period is 2018-2025, covering 1,991 trading days with either daily or monthly rebalancing. Only the optimized portfolios incur costs: 0.10% of gross turnover, without halving turnover.

At the three-month window with daily rebalancing, Taş reports net, zero-risk-free Sharpe ratios of 1.308 for HF-MVP 30m and 1.304 for HF-MVP 5m. Daily-MVP returns 1.213. The equal-weighted book, charged no trading costs, returns 1.121. The paper qualifies the result carefully: "high-frequency covariance estimates do not provide unconditional dominance."

Less trading at every window

Changing the window leaves the turnover ordering intact. With daily rebalancing and a 12 months window, HF-MVP 30m turns over 0.52% per day, compared with 1.15% for Daily-MVP. At 6 months, the comparison is 1.11% against 2.54%; at 1 month, it is 7.70% against 13.82%. Monthly rebalancing gives the same ordering throughout. At 3 months, for example, turnover per rebalance is 23.22% against 36.60%. HF-MVP 5m trades less still.

For the three-month daily figures, Taş gives annualized turnover of roughly 600% for HF-MVP 30m and 1,350% for Daily-MVP. Charging 0.10% a unit makes those additional 750 points cost Daily-MVP about 0.75 percentage points annually. CAGR is 41.77% against 38.27%, a gap of 3.5 points. Costs account for a fifth of that gap. Gross return supplies the rest, and the evidence for that part is thin.

The paper reports turnover for every optimized cell.

Does the Sharpe advantage survive six months?

Barely. With daily rebalancing at 6 months, Daily-MVP has a Sharpe of 1.267, compared with 1.279 for HF-MVP 30m. HF-MVP 5m falls below the daily version at 1.262. Six months is also the best window for Daily-MVP. Taş acknowledges the selection directly: "the 3-month results therefore describe the configuration most favorable to high-frequency inputs rather than a typical outcome."

His defence is that both HF variants reach their best results at three months while trading much less than at one month. That gives a reason to show the three-month cell. But matching it against Daily-MVP at three months, away from that method's peak, favours HF. Compare each method at its best window and the Sharpe gap is 1.308 against 1.267, or 0.041. Those windows were selected after the fact from a grid of four. The paper defers "multiple-comparison and Sharpe-difference tests" to future work.

Drawdown weakens the HF case too. At three months with daily rebalancing, maximum drawdown is -22.25% for Daily-MVP and -24.04% for HF-MVP 30m. With monthly rebalancing, the figures are -17.56% against -21.15%.

Concentration offers some reassurance. At the three-month window with daily rebalancing, HF-MVP 30m averages 6.23 effective names, compared with 5.90 for Daily-MVP. It holds an average of 2.29 stocks at the 20% cap, against 2.86 for Daily-MVP. The HF returns therefore come without concentrating the portfolio in fewer names.

Dollars and purchasing power

HF-MVP 30m earns a cumulative 1476.05% in nominal TRY. Converted to USD, that becomes 39.01%; in real terms, it becomes 46.91%. Daily-MVP's 1193.85% becomes 14.12% USD. The conversions reduce the scale of the gains while preserving their order. Every cumulative TRY wealth multiple in the table is divided by the same factor, about 11.34 for USD and about 10.73 for real terms. Conversion cannot change the ranking. These columns resize the returns without testing anything further.

The same-stock buy-and-hold gives the useful comparison: 25.87% in USD and 33.02% real, versus 39.01% and 46.91% for HF-MVP 30m. The BIST 30 Total Return Index earned 2.80% in USD. Whatever the survivor filter contributed is included in the 23-point gap (25.87% vs 2.80% in USD). Taş identifies a "continuous-data sample-selection or survivorship concern" and says index comparisons "should be interpreted as benchmark comparisons". Requiring continuous 5-minute data through 2025 selects stocks using information available only at the sample's end.

Why we could not rerun the study

Our data covers US equities only. We have neither intraday nor daily prices for these Borsa Istanbul listings, nor the BIST 30 Total Return, USD/TRY or Turkish CPI series. Rebuilding 30-minute covariance from minute bars on US stocks would be possible. That would test whether the idea carries to another market.

Keep the turnover finding.

The trading case has less support. It relies on 11 survivor-selected names and a flat 0.10% cost, with no allowance for spread or impact. At three months, HF-MVP 30m has a Sharpe advantage of about 0.1 (1.308 vs 1.213). At six months, that advantage is 0.012, and HF-MVP 5m trails Daily-MVP. A Sharpe-difference test using a broader point-in-time BIST universe would change our view if the HF advantage remained above Daily-MVP's best window. Until then, the defensible use is narrower. In this 11-stock sample, intraday covariance lowered daily-rebalanced turnover from about 1,350% to 600% a year at the same volatility. Monthly turnover fell from 440% to 280%.