Abstract
This study empirically examines the risk–return trade-off under Modern Portfolio Theory (MPT) using Borsa İstanbul (BIST) data. Comparing annualized Sharpe ratios, maximum drawdowns and win rates across factor portfolios shows that risk-adjusted — not raw — performance is what matters. The low-volatility portfolio offers a defensive profile with the smallest drawdown (-30.2%), while momentum strikes an aggressive balance with the highest Sharpe (2.50). Diversification, equal weighting and drawdown management are discussed.
1. Introduction
Markowitz’s (1952) mean-variance framework casts portfolio choice as a trade-off between expected return and risk. Rational investors prefer ‘efficient’ portfolios that maximize return for a given risk. We ask: does high return always require high risk on BIST, or is risk-adjusted superiority attainable?
2. Theoretical Framework and Literature
- Mean-variance: Markowitz (1952) — diversification reduces risk without sacrificing return; defines the efficient frontier.
- Safety-first: Roy (1952) — minimize the probability of disaster.
- Sharpe ratio: Sharpe (1964, 1966) — excess return per unit of total risk.
- Sortino ratio: Sortino & van der Meer (1991) — penalizes only downside.
- Diversification: Statman (1987) — how many stocks are enough.
- Risk parity: Qian (2005) — equalize risk contribution, not capital.
3. Data and Methodology
The sample covers liquid BIST equities over ~10 years (2016-01-04–2026-07-23). Five systematic portfolios (momentum, low volatility, value, dividend+quality, multi-factor ML), each 17–20 equal-weighted stocks, are evaluated via Sharpe ratio, maximum drawdown and win rate versus the BIST 100. Limitations: backtest basis; simplified costs; Sharpe assumes normality while BIST returns can be fat-tailed; single regime.
4. Findings
Over the same window the BIST 100 returned 32.9% (trailing 12m) and reached ~20× over the sample. Table 1:
- Momentum — Sharpe: 2.50 · Max drawdown: -45.3% · Win rate: 69% · Annualized: +141.6%
- Low Volatility — Sharpe: 1.91 · Max drawdown: -30.2% · Win rate: 70% · Annualized: +29.4%
- Value (E/P) — Sharpe: 1.44 · Max drawdown: -49.0% · Win rate: 67% · Annualized: +23.2%
- Dividend + Quality — Sharpe: 1.94 · Max drawdown: -37.6% · Win rate: 66% · Annualized: +25.8%
- Multi-factor (ML) — Sharpe: 3.02 · Max drawdown: -36.9% · Win rate: 79% · Annualized: +96.4%
Momentum posted the highest Sharpe (2.50) but a deep drawdown (-45.3%); low volatility combined the smallest drawdown (-30.2%) with a high win rate (70%) — an attractive defensive profile.
5. Discussion
The evidence supports MPT’s core claim: judge return relative to risk. Two portfolios with similar nominal returns are not equivalent — the one with the shallower drawdown is more ‘livable’ because it triggers less panic. Drawdown is path-dependent and captures loss aversion better than volatility. Equal-weighted 17–20 stock portfolios remove most idiosyncratic risk but not systematic risk; because factors lead in different regimes, multi-factor diversification adds value.
6. Conclusion and Limitations
Risk-adjusted metrics belong at the center of portfolio evaluation. On BIST, momentum was aggressive and low volatility defensive; the ‘best’ portfolio depends on risk tolerance. Read cautiously given the backtest basis, simplified costs and Sharpe’s normality assumption. Not investment advice.
References
- Markowitz, H. (1952). Journal of Finance, 7(1).
- Roy, A. D. (1952). Econometrica, 20(3).
- Sharpe, W. F. (1964). Journal of Finance, 19(3).
- Sharpe, W. F. (1966). Journal of Business, 39(1).
- Sortino & van der Meer (1991). Journal of Portfolio Management, 17(4).
- Statman, M. (1987). Journal of Financial and Quantitative Analysis, 22(3).
- Qian, E. (2005). PanAgora Asset Management.
