2자산 효율적 프론티어 계산기
무료 2자산 효율적 프론티어 계산기: 수익률, 변동성, 상관관계를 조정하여 두 자산에 대한 효율적 프론티어, 최소분산 포트폴리오, 접점포트폴리오를 그리세요.
이 도구가 마음에 드시나요? portfolios.tools를 영원히 무료로 유지하는 데 도움을 주세요.
작동 방식
The 2 Asset Efficient Frontier tool plots all possible portfolios you can create by combining two assets in varying proportions. For each weight combination from 0% to 100% in Asset A, the tool computes the portfolio's expected return and risk (standard deviation), then plots them on a risk return chart. Set Asset A at 10% return and 20% vol, Asset B at 6% return and 10% vol, correlation 0.3. The frontier curve shows every blend from 100% A to 100% B with computed risk and return. Try correlation 0.8 versus 0.2 with same asset stats to visualize diversification benefit as frontier bulge toward lower risk. Expected returns are forward assumptions you supply, not historical averages pulled from data feeds. Use conservative return estimates when teaching mean variance concepts because optimistic inputs shift tangency toward higher risk assets. Set Asset A at 10% return and 20% vol, Asset B at 6% return and 10% vol, correlation 0.3. The frontier curve shows every blend from 100% A to 100% B with computed risk and return.
The resulting curve is the efficient frontier. The tool also identifies two key portfolios: the minimum variance portfolio (lowest possible risk) and the tangency portfolio (highest possible Sharpe ratio). Adjust the six inputs: each asset's return and volatility, their correlation, and the risk free rate: to see how the frontier and optimal portfolios change in real time. Minimum variance portfolio minimizes vol regardless of return. Tangency portfolio maximizes Sharpe ratio and sits where a ruler from the risk free rate touches the frontier tangentially. Capital Market Line connects risk free rate to tangency portfolio and dominates all other risky mixes when you can lend and borrow at the risk free rate. Points below the frontier represent inefficient mixes you would never choose if you trust the input assumptions. Hover chart points to compare return and risk at each weight split between the two assets. Minimum variance portfolio minimizes vol regardless of return. Tangency portfolio maximizes Sharpe ratio and sits where a ruler from the risk free rate touches the frontier tangentially.
Capital Market Line connects risk free rate to tangency portfolio and dominates all other risky mixes when you can lend and borrow at the risk free rate. Points below the frontier represent inefficient mixes you would never choose if you trust the input assumptions. Hover chart points to compare return and risk at each weight split between the two assets. Minimum variance portfolio minimizes vol regardless of return. Tangency portfolio maximizes Sharpe ratio and sits where a ruler from the risk free rate touches the frontier tangentially.
입력값이 변경될 때마다 2자산 효율적 프론티어을(를) 사용하세요: 시장 변동, 새로운 기여금 또는 수정된 개인 가정 후. 소프트웨어 설치 없이 빠른 재실행을 위해 페이지를 북마크하세요.
단계별 안내
- 2자산 효율적 프론티어을(를) 열고 현재 입력값을 입력하세요.
- 계산된 출력과 요약 테이블을 검토하세요.
- 가정을 조정하고 시나리오를 나란히 비교하세요.
실전 예제
Example scenario for 2-Asset Efficient Frontier: 0%, 100%, 10%. Enter those values above to reproduce the walkthrough described in How it works.
한 번에 하나의 입력을 조정하여 민감도를 확인하세요. 2자산 효율적 프론티어은(는) 즉시 업데이트되므로 행동하기 전에 낙관적 및 보수적 가정을 스트레스 테스트할 수 있습니다.
이 계산기를 사용할 때
Reach for 2-Asset Efficient Frontier when plot the efficient frontier, minimum variance portfolio, and tangency portfolio for any two assets: adjust return, volatility, and correlation.. It suits quick what if analysis before trades, allocation changes, or plan updates.
결정이 세금, 유동성 또는 하나의 공식이 포착하는 것 이상의 다년 전망을 포괄할 때 관련 도구와 함께 사용하세요.
흔한 실수
입력 단위나 오래된 시장 가격을 확인하지 않고 출력을 복사하는 것은 2자산 효율적 프론티어에서 흔한 오류입니다. 행동하기 전에 티커, 백분율 및 날짜를 확인하세요.
단일 기준 시나리오만 실행하면 꼬리 위험을 무시합니다. 보수적 입력으로 스트레스 테스트하고 결정이 중요할 때 아래 나열된 관련 도구와 비교하세요.
공식
rₚ = wₐ × rₐ + (1 − wₐ) × rᵇ
σₚ² = wₐ²σₐ² + (1−wₐ)²σᵇ² + 2ρσₐσᵇwₐ(1−wₐ)
wₘᵢₙ = (σᵇ² − ρσₐσᵇ) / (σₐ² + σᵇ² − 2ρσₐσᵇ)
Max Sharpe = w that maximizes (rₚ − rᶒ) / σₚ
제한 사항 및 가정
2-Asset Efficient Frontier uses simplified assumptions for transparency and speed. Real outcomes include fees, taxes, timing, and data errors not fully modeled here. Treat outputs as estimates, not guarantees.
주요 용어
- What is the efficient frontier
- The efficient frontier shows the set of portfolios that offer the highest expected return for a given level of risk.
- What is the minimum variance portfolio
- The minimum variance portfolio is the combination of two assets that produces the lowest possible portfolio volatility.
- 모델 가정
- The tangency portfolio is the point on the efficient frontier that maximizes the Sharpe ratio: excess return per unit of risk.
대안 비교
Measure Sharpe with Sharpe Sortino Ratio Calculator. Use those calculators when 2-asset efficient frontier alone does not capture the full decision.
portfolios.tools의 내부 링크는 계산기 체인을 도와줍니다: 먼저 2자산 효율적 프론티어을(를) 실행한 다음, 아래 관련 섹션의 전문 도구로 엣지 케이스를 검증하세요.
FAQ
What is the efficient frontier?
The efficient frontier shows the set of portfolios that offer the highest expected return for a given level of risk. Each point on the curve is a different combination of Asset A and Asset B. Portfolios below the frontier are suboptimal because you could achieve a higher return for the same risk or lower risk for the same return. Portfolios inside the frontier are inefficient: you could get more return for the same risk by moving toward the curve. Real portfolios with estimation error in inputs may appear inside the frontier ex post even when ex ante they looked optimal. Markowitz mean variance framework assumes investors care only about expected return and variance, ignoring higher moments like skewness and kurtosis. Portfolios inside the frontier are inefficient: you could get more return for the same risk by moving toward the curve.
What is the minimum variance portfolio?
The minimum variance portfolio is the combination of two assets that produces the lowest possible portfolio volatility. Its weight depends on the two assets' volatilities and their correlation. Mathematically, it is found by setting the derivative of portfolio variance with respect to weight to zero. With negative correlation, min variance weight can exceed 100% or go negative, implying shorting for theoretical hedged portfolios. Long only investors cap weights between 0% and 100% even when unconstrained formula suggests otherwise. Min variance is not always the same as minimum drawdown portfolio, which depends on path dependent return sequences and tail events. With negative correlation, min variance weight can exceed 100% or go negative, implying shorting for theoretical hedged portfolios.
What is the tangency portfolio?
The tangency portfolio is the point on the efficient frontier that maximizes the Sharpe ratio: excess return per unit of risk. It is also called the optimal risky portfolio. When combined with the risk free asset, the tangency portfolio gives you the Capital Market Line (CML), which dominates all other frontier portfolios. Tangency weights change when risk free rate rises. Higher rates tilt optimal risky portfolio toward lower vol assets. Sharpe ratio uses entered expected returns, so poor return forecasts shift tangency materially. Investors who cannot borrow at the risk free rate may hold a mix below tangency on the frontier instead. Tangency weights change when risk free rate rises. Higher rates tilt optimal risky portfolio toward lower vol assets.
How does correlation affect the frontier?
Correlation measures how two assets move together, ranging from negative one (perfectly opposite) to positive one (perfectly together). Lower correlation produces more diversification benefit: the frontier bulges more to the left. At correlation equals negative one, you can achieve zero portfolio risk with the right weights. Correlation one eliminates diversification benefit: frontier becomes a straight line. Correlation below 0.5 visibly bends the curve leftward. During 2008 style crises correlation toward one shifts realized frontier left versus ex ante estimates. Use conservative correlation assumptions when stress testing retirement portfolios. Rolling correlation estimates change with sample window length and materially move min variance and tangency weights. Correlation 1 eliminates diversification benefit: frontier becomes a straight line. Correlation below 0.5 visibly bends the curve leftward.
Which portfolio should I choose?
You can test different values by adjusting the sliders. Try high return and high vol for A versus low return and low vol for B. Vary the correlation to see how the frontier shape changes. The tangency dot moves based on the risk free rate: a higher risk free rate pushes you toward lower risk assets. Choose tangency for max risk adjusted return, min variance for capital preservation, or a custom blend matching your return target. Combine with Risk Parity Allocator when expanding beyond two assets into multi asset policy portfolios. Historical mean return inputs often overstate forward frontier location because past winners dominate simple averages. Export key portfolio weights from the results panel for notes or classroom assignments. Choose tangency for max risk adjusted return, min variance for capital preservation, or a custom blend matching your return target.
이 2자산 효율적 프론티어 계산기를 휴대폰이나 태블릿에서 어떻게 사용하나요?
예. 이 도구는 데스크톱과 동일한 공식으로 모바일 브라우저에서 완전히 실행됩니다. 선택적 localStorage는 브라우저 설정에서 활성화된 경우 기기에 입력값을 기억할 수 있습니다.
2자산 효율적 프론티어을(를) 사용할 때 내 데이터는 어디에 저장되나요?
당사 서버 어디에도 없습니다. 계산은 브라우저에서 로컬로 실행됩니다. 선택적 localStorage는 기기에서만 양식 필드를 저장하며 네트워크를 통해 포트폴리오 번호를 전송하지 않습니다.
세금 또는 법적 결정에 2자산 효율적 프론티어에 의존해야 하나요?
아니요. 이 도구는 교육용 수학만 제공합니다. 세법, 계좌 규칙 및 개인 상황은 다양합니다. 중대한 결과를 초래하는 거래 전에 자격을 갖춘 세무 또는 법률 전문가와 상담하세요.
관련 도구
Measure Sharpe with Sharpe Sortino Ratio Calculator. Assess drawdowns with Maximum Drawdown Calc. Expand beyond two assets with Risk Parity Allocator on portfolios.tools when building multi asset policy portfolios beyond this two asset teaching model for retirement, institutional asset allocation study, and classroom exercises. Measure Sharpe with Sharpe Sortino Ratio Calculator. Assess drawdowns with Maximum Drawdown Calc. Expand beyond two assets with Risk Parity Allocator.