Nikolas
Dion Savio

Can macroeconomic variables reliably predict investment-grade corporate bond excess returns? This project built a full machine learning forecasting pipeline using 30 years of monthly FRED data (1996–2026), targeting the IG OAS-implied excess return over equivalent-duration US Treasuries.

The focus was on methodologically rigorous out-of-sample evaluation, mimicking the constraints a real fixed-income PM would face.

• Target variable: Monthly IG corporate bond excess return over duration-matched Treasuries
• Predictors: 10Y–2Y Treasury term spread, IG option-adjusted spread (OAS), VIX, Fed Funds Rate, CPI YoY, real GDP growth rate, unemployment rate - all lagged one month to prevent look-ahead bias
• StandardScaler applied inside each cross-validation fold to prevent data leakage
• TimeSeriesSplit (5 folds) used for all hyperparameter tuning - respecting the temporal ordering of observations

• Rolling-window OLS (60-month window) - used as interpretable baseline
• LASSO regression - L1 penalty shrinks irrelevant predictors to zero; alpha tuned via cross-validation
• LASSO consistently selected the term spread and OAS as the two dominant predictors - consistent with the academic literature on credit risk premia
• Evaluation metrics: out-of-sample R², Mean Absolute Error (MAE), directional accuracy

Implemented the Avellaneda–Stoikov (2008) model - the seminal academic framework for optimal market-making - from mathematical first principles. The model solves a stochastic control problem to find the bid and ask prices that maximise expected terminal wealth, explicitly penalising inventory accumulation.

The mid-price follows arithmetic Brownian motion: dS = σ dW. The market maker posts quotes at distances δᵃ (ask) and δᵇ (bid) from the mid-price. Orders arrive as Poisson processes with intensity λ(δ) = Ae^(−κδ).

• Reservation price: r(s,q,t) = s − q · γ · σ² · (T−t) - shifts quotes to reduce inventory risk
• Optimal half-spread: δ* = (γσ²(T−t))/2 + (1/γ) · ln(1 + γ/κ) - widens with risk aversion γ
• Key insight: the optimal strategy is not symmetric - it leans quotes based on current inventory to mean-revert position

Observe how the spread widens when inventory accumulates (protecting against adverse selection) and tightens when near zero - consistent with the model's theoretical predictions.

Applied statistical and econometric methods to financial market data as part of Imperial MSc Financial Statistics coursework. Estimated CAPM beta for IBM against the S&P 500 using OLS on excess returns and tested moving average signal predictability via a hit-ratio Z-test. Also fitted CIR and Vasicek short-rate models to US and UK 3-month rates (1980-2000), comparing mean-reversion speed, volatility, and in-sample fit.

• S&P 500 (SPY) - daily price and log-returns, Jan 2010–Dec 2025
• GBP/USD - daily spot rate and log-returns
• US 3-Month T-Bill rate - weekly, Federal Reserve H.15
• US 10-Year Treasury Yield - daily, FRED
• 10Y–3M Term Spread - derived series, used as recession predictor

• Stationarity: ADF and KPSS tests - all price/yield levels non-stationary (I(1)); first-differenced log-returns stationary at 1% significance
• S&P 500 returns: auto.ARIMA selected ARIMA(1,0,0) - slight positive autocorrelation at lag 1 (AR coefficient: 0.06); ARCH-LM test confirms volatility clustering → GARCH(1,1) fitted with β = 0.91
• GBP/USD: ARIMA(0,1,0) - effectively a random walk; no exploitable linear structure in returns
• Term spread: ARIMA(2,0,0) with significant short-run predictability; mean-reverts with half-life ~18 months
• GARCH(1,1) β estimates of 0.88–0.92 across equity series confirm high volatility persistence - shocks decay slowly

Only lag 1 exceeds the 95% confidence interval - consistent with weak-form efficiency. The AR(1) structure is statistically present but economically small (AR coefficient 0.06), confirming that S&P 500 returns are largely unpredictable from their own history.

Implemented and backtested two quantitative strategies on Pfizer (PFE) in R: a Moving Average Crossover (MAC) with optimised fast/slow windows, and a Bollinger Band Breakout. Enforced a 1-day execution lag on all signals, modelled transaction costs, and used charts.PerformanceSummary() for unbiased performance attribution. The Bollinger strategy outperformed MAC on a risk-adjusted basis, suggesting mean-reversion signals hold an edge over trend-following on single-stock data.

• Signal: Golden Cross (50-day SMA crosses above 200-day SMA) → long; Death Cross → flat/cash
• Critical design choice: 1-day execution lag on all signals - signals generated on day t are executed at open on day t+1, reflecting realistic market access
• Transaction costs: 5 basis points per side (10bp round trip) modelled on all trades
• Assets tested: SPY (S&P 500 ETF), AAPL, MSFT - January 2010 to December 2024
• Benchmark: Buy-and-hold with equivalent capital and same start date

Key insight: The MA crossover strategy sacrifices return for drawdown protection - it sidesteps the worst of the COVID crash (−19% vs −34% drawdown). This makes it a useful risk management overlay rather than an alpha-generating strategy in its own right.

Produced a comprehensive equity valuation and capital-structure assessment of Diageo plc (LSE: DGE) as part of Imperial College MSc Risk Management & Valuation coursework. Diageo, formed from the 1997 merger of Grand Metropolitan and Guinness, was in the midst of a strategic pivot: divesting Pillsbury and Burger King to concentrate on its higher-margin beverage alcohol portfolio (Spirits & Wine, Guinness Brewing).

The analysis spanned four workstreams: (1) historical KPI diagnostics across FY98–FY00, (2) a ground-up DCF valuation, (3) financial policy and capital-structure analysis, and (4) an execution plan for the transition from A/AA to BBB credit.

Analysed 10 KPIs across three fiscal years to establish the normalised operating baseline for the DCF. Despite broadly flat top-line growth (−1.9% FY99, +0.6% FY00), Diageo expanded EBIT margins from 15.5% to 17.2% through operating leverage and mix improvement. Spirits & Wine contributed 50.6% of FY00 EBIT, confirming the strategic rationale for the beverage focus.

Free cash flow generation was strong (FY00: £865m) with ROIC improving from 11.0% to 12.6%. Interest coverage held comfortably at 5.2–6.1x, well within the BBB–A band.

Constructed Free Cash Flow to the Firm from reported financials: FCFF = CFO + Interest×(1−t) − Net CapEx. Used the 3-year average (£916m) rather than the elevated FY00 figure (£1,152m) to avoid over-weighting a single year’s favourable tax timing.

The 5-year explicit forecast (FY01–FY05) ramped revenue growth conservatively from 0.5% to 2.0%, held EBIT margin constant at 17.2%, and applied the historical FCFF/EBIT conversion ratio. Terminal value was computed via Gordon Growth (g = 2.5%) and discounted at WACC = 8.0%.

Result: Implied equity of £10.5bn versus an observed market cap of £20.1bn. The terminal value accounts for 76.7% of enterprise value, making it a key sensitivity driver tested in the heatmap below.

Benchmarked Diageo against 12 listed peers across its four business segments (spirits, beer, food, restaurants), weighting EV/EBIT multiples by each segment’s revenue contribution. The revenue-weighted blended multiple of 13.5x applied to FY00 EBIT (£2,043m) implied an equity range of £17–24bn, tightly bracketing the observed £20.1bn market cap and validating the comps as the more reliable valuation anchor for a mature, cash-generative business.

Stress-tested the DCF across a WACC range of 6.5–9.5% and terminal growth of 1.0–4.0%. At the base case (WACC = 8.0%, g = 2.5%), implied equity is £10.5bn. Narrowing WACC by 100bps or raising g by 50bps each adds roughly £2–3bn, demonstrating the model’s high sensitivity to terminal assumptions, which is precisely why the comps cross-check is essential.

The football field chart consolidates all methodologies: the DCF provides a conservative fundamental floor, while the EV/EBIT comps range brackets market consensus.

Assessed Diageo’s transition from an A/AA credit profile (inherited from Guinness and Grand Metropolitan) to a BBB target, justified by static trade-off theory. The beverage-alcohol core’s low cash-flow volatility (~2.3%) supports higher leverage. Monte Carlo simulation of EBIT scenarios confirmed the optimal interest-coverage corridor at 5–8x, between the BBB median of 4.94x and the A median of 8.34x.

Diageo returned £2.8bn via buybacks in FY98 and £1.2bn in FY99, alongside stable dividends of £674–835m per year. Sustainable growth rate (~5%) significantly exceeded actual asset growth (negative), confirming excess free cash generation that funded the re-levering programme.

The £9.7bn gap between the DCF base case (£10.5bn) and observed market cap (£20.1bn) is primarily explained by three factors: (1) the normalised FCFF base understates FY00 actual cash flow by ~£3bn in present-value terms, (2) the conservative 2.5% terminal growth may underweight Diageo’s brand pricing power, and (3) the market prices strategic option value, including the expected £130m/year cost synergies from the beverage focus, future M&A upside, and a conglomerate-to-pure-play re-rating.

• DCF as a floor: The normalised-FCFF approach deliberately provides a conservative anchor (£10.5bn); it is not meant to match the market price but to establish a fundamental lower bound
• Comps as the primary benchmark: The revenue-weighted blended EV/EBIT of 13.5x (vs Diageo’s actual 13.7x) confirms the market is pricing the stock consistently with peers
• Capital structure aligned with strategy: The BBB transition is sound: low cash-flow volatility, coverage within the 5–8x corridor, and excess FCF fund shareholder returns without straining the balance sheet
• Strategic optionality drives the premium: The market’s willingness to pay 2x the DCF floor reflects credible expectations of cost synergies, portfolio focus, and acquisition-driven growth

Completed the Oxford Saïd Private Markets Investments Programme, covering the full private equity investment cycle from deal origination through exit. The centrepiece was a detailed LBO model for InfraCo - an infrastructure business - building an integrated financial model with a 7-year hold, capex-driven debt structuring, operating leverage analysis, and exit return attribution. Extended the model to a secondary buyout (rebuy) scenario and benchmarked returns against public market equivalents (PME) using the Kaplan-Schoar methodology.

• Target: InfraCo - infrastructure asset with regulated revenue and high EBITDA margins (50-53.5%)
• Entry: EV £562mm at 11.2x EV/EBITDA; funded £300mm acquisition debt + £272mm equity (50/50 SHL/common)
• Growth driver: 8% revenue CAGR years 1-4, tapering to 4% years 5-7 via capex-funded asset expansion
• Debt structure: £300mm fixed acquisition debt at 4%; capex facility drawn annually to £191mm by year 7 at 6x leverage target
• Exit: Year 7 at 11.0x EV/EBITDA; exit equity proceeds £442mm on £272mm entry - IRR 13.01%
• Secondary buyout: Modelled rebuy scenario at entry 11x yields 8.38% long-run IRR, with sensitivity from 10x (10.4%) to 12x (6.9%)

Exit multiple sensitivity confirms the transaction is robust across a range of outcomes. At the base case 11x exit, IRR is 13.01%. The model stress-tests entry pricing from 10.0x to 12.0x on the rebuy - illustrating the multiple compression risk that compresses LP returns on secondary buyouts where entry valuations are elevated.

Benchmarked against S&P 500 and MSCI Europe using the Kaplan–Schoar PME methodology. Base case generates a PME of 1.34 - implying the strategy outperforms a public market equivalent by 34% on invested capital, justifying the illiquidity premium demanded by institutional LPs.

Optiver's Optibook is the simulated exchange Optiver uses to benchmark quantitative traders. The dual-listing challenge presents the same underlying asset on two distinct order books - a liquid "main" listing and an illiquid "dual" listing. Long-run convergence is guaranteed by no-arbitrage, but short-term divergence creates two complementary edges - arbitrage across the books and market making on the illiquid side. The objective is to convert these edges into PnL while respecting hard exchange limits on position, outstanding orders, and message rate.

• Cross-book arbitrage: when the dual's best bid crosses the main's best ask (or vice versa), the bot lifts the cheap leg and hits the expensive one, capturing the spread net of competition and hedge slippage before the books realign
• Passive market making on the dual: the main listing's mid-price is treated as the fair value, and the bot continuously quotes both sides of the dual at offsets that widen with inventory to encourage mean reversion to flat
• Inventory-aware quote skewing: bid and ask offsets adjust as a function of net position rather than staying symmetric, so the resting book is naturally pulled back toward zero exposure
• Real-time delta hedging: every fill on the dual leg triggers an offsetting order in the main leg, keeping net delta close to zero before the exchange's soft-delta mechanism intervenes

• Position limit: ±100 lots per instrument - the bot tracks live position from fills and refuses any order that would breach the cap
• Outstanding order cap: 200 lots resting per instrument - quote sizes and refresh logic are tuned to stay inside this envelope
• Message rate: 25 inserts, deletes, and amends per second combined - the main loop batches updates and avoids quote thrashing when the fair value barely moves
• Soft delta limit: any unhedged delta above 100 for more than 10 seconds is auto-hacked at 2% off mid, so hedging latency is treated as a hard requirement rather than best-effort

The bot is written in Python against Optiver's Optibook API. The core loop subscribes to order book updates, recomputes the fair value and target quotes, and emits the minimum set of insert, cancel, and amend messages needed to align the live book with the target. Position, working orders, and last-quoted levels are maintained in lightweight in-memory state so the loop stays tight enough to react inside the exchange's rate budget. The architecture is built to extend cleanly to multiple instrument pairs running in parallel.

Stress-tested the dual-listing algorithm across 10 parameter configurations × 10 random seeds each, with every run a 5,000-tick synthetic session driven by a regime-switching order-book model (normal, volatile, illiquid, informed). The harness lives in dual_listing/aggressive_backtest_harness.py. Stats below are aggregated across the full 100-run sweep, not cherry-picked from the best configuration. The synthetic model is mine, not Optiver's, so these numbers validate the execution, hedging, and rate-limit logic under stress rather than prove a live trading edge. The real test is the Optibook leaderboard.

Figure 1: Cumulative PnL Across the 100-Run Backtest Sweep (10 Configs × 10 Seeds)

The shaded band covers the central 80% of cumulative PnL paths across all 100 sessions. PnL accrues steadily from passive market-making revenue, with occasional steeper segments where the regime briefly flips to illiquid or informed and the cross-book arbitrage leg captures wider edges. The 10th percentile path stays positive throughout, so the execution logic holds up even on the most adverse seed rather than depending on a few lucky sessions. Because the generator carries a built-in spread, the point of the sweep is not that it makes money but that the bot harvests that spread cleanly without breaching limits or blowing out inventory under every regime.

• Robust across seeds: mean PnL 2,471, median 2,483, with a P10–P90 spread of 1,649–3,281 - the distribution is tight enough that the median is a fair summary, not a few lucky tails carrying the average
• Drawdowns small relative to terminal PnL: mean peak-to-trough drawdown of 12.8 against a median end-of-session PnL of 2,483 (≈0.5% of terminal), with a worst-case drawdown of 29.7 on the most adverse seed
• Tick-PnL risk-adjusted score: median 6.46, computed as mean(ΔPnL) / σ(ΔPnL) × √1000 on simulated tick-by-tick PnL changes. This is a within-simulation diagnostic only, not a real-trading Sharpe ratio - the √1000 is an arbitrary fixed scaling, not an annualisation
• Clean rate-limit compliance: zero request-budget overruns across 500,000 simulated ticks, validating that the message-batching logic stays inside the 25/sec exchange envelope under all four regime states