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The document explains two possible budget constraints in mean-variance portfolio optimization when short sales are permitted. Requiring signed portfolio weights to sum to one treats short positions as negative weights whose proceeds can fund long positions.…
The document considers a finite-difference approximation to the Black–Scholes equation and asks how coefficient sign conditions can establish a maximum-norm bound. The proposed argument rewrites each value at one time level using the neighboring values and…
The document introduces mean-variance portfolio optimization, including a minimum-variance portfolio and a variance-minimizing portfolio constrained to a target expected return. It then describes practical variations: long-only holdings, caps on individual…
The document discusses the economic meaning of the intercept, or alpha, in regression-based asset pricing models. In a return regression, the intercept represents the component of return not explained by the included factors when their returns are zero. For…
The document considers how to recover FX option strikes from broker volatility quotes, forward points, deposit rates, and delta conventions. It explains that the ATM strike formula depends on the convention: a delta-neutral strike with premium-adjusted delta…
The document explains how to obtain a quantile of an exponentiated normally distributed variable. If the logarithm of a positive variable is normal, its quantile is found by taking the exponential of the corresponding normal quantile. Because the exponential…
The document raises a problem in simulation-based testing of investment strategies that use valuation measures such as price-to-book or dividend yield. A simulation that generates prices while retaining historical values for accounting variables may create…
The document examines why selecting the top decile of S&P 500 stocks by price-to-earnings ratio can produce fewer names than an expected count. One proposed explanation is that some companies had negative earnings during the measurement period. Since the…
The document asks how to interpret a bond investment denominated in one currency when the investor hedges the currency exposure using a forward rate whose implied yield differs from the bond’s yield. It frames the question as whether a 10% bond yield…
The document asks for a route from beginner-level C++ to quantitative trading, from a learner who already programs professionally in Visual Basic and has trading experience. The response suggests starting with a general C++ text, then studying resources…
The document asks how to interpret the point where a line from the risk-free rate touches the efficient frontier for a portfolio built from three stocks. In mean-variance portfolio theory, that tangency point represents the risky portfolio with the highest…
The document examines how the value of an inflation-linked payment can differ from expected inflation multiplied by a discount factor when inflation and interest rates are correlated. It presents a simplified convexity adjustment for a fixing paid after a…
The document asks whether historical listed SPX options data from the CBOE data shop is reliable enough for backtesting, especially regarding missing or incorrect prices and Greeks. The response recommends checking a small sample of purchased contracts…
The document examines limitations of variance as a portfolio risk measure, especially when return distributions are not well described by a stable normal model. One example compares two hypothetical single-stock portfolios with the same variance: one has…
The document asks whether investors who understand asset pricing should hold only portfolios on the mean-variance efficient frontier. It presents a relation between an asset’s expected return, its volatility, its correlation with the stochastic discount…
The document explains how to maximize expected return for a portfolio subject to a limit on expected shortfall (ES), also called conditional value-at-risk. It describes an auxiliary function of portfolio weights and a threshold variable: the function is…
The document explains why spot forex historical data cannot be interpreted like exchange consolidated equity data. Spot foreign exchange is fragmented across dealers and electronic venues, so there is no single source that captures all quotes, orders,…
The document applies Itô’s lemma to an exponential function of an integrated short rate under the Vasicek model. It derives the stochastic differential of the intermediate process, then uses its drift and diffusion terms to obtain the dynamics of the…
The document considers whether historical equity prices should be adjusted for ordinary dividends when backtesting strategies, alongside the existing adjustments for splits and special dividends. Its practical guidance separates signal construction from…
The document explains how the Lévy measure determines whether successive jump times and their gaps can be treated as discrete events. When the Lévy measure has finite total mass, jumps form a compound Poisson process, with rate equal to that total mass; the…
The document answers whether a bond can begin amortizing after an initial period of interest-only payments. It confirms that such structures exist, while noting that they do not have a single standard name in the response. The timing and pattern of principal…
The document considers how to compute an exponential moving average across a large universe without replaying every observation since each security began trading. It explains that the recursive form needs only the prior EMA, while the equivalent direct form…
The document asks how to combine multiple strategies into one portfolio and why volatility calculated from aggregate asset exposures may differ from volatility calculated using strategy return streams. It describes two views: treat each strategy’s returns as…
The document compares ways to calculate a bond’s yield to maturity from price when repeated updates make speed important. One approach computes yields for three selected prices, fits a quadratic price–yield relationship, and uses it to estimate yields for…