Markku

We demonstrate how simple long-term volatility forecasts can be improved by incorporating the volatility of short-term volatility into forecasting models. The theoretical framework for modelling volatility of short-term volatility, along with its role in long-term forecasts, will be outlined. Empirical tests will then illustrate the value of including volatility of volatility measures in practice. A …

Employing volatility of volatility in long-term volatility forecasts Read More »

Can we find inflation hedges in the stock market? The answer is yes—at least to some extent. We find that certain industries, particularly those related to resource equities, have historically offered some protection against high inflation levels. In periods when inflation was largely driven by oil and energy crises, these industries also hedged against rising …

Hedging inflation in the stock market Read More »

Last edit on 24-Mar-2025 Are stocks an inflation hedge? At least in the long run? We find the answer to both questions is no. While fundamental returns—comprising dividend return and earnings growth—do help hedge inflation, valuation changes undermine this hedge. This holds true whether we examine yearly returns, ten-year returns, or anything in between. Stocks …

On inflation and stock returns Read More »

Constructing a high Sharpe ratio portfolio, paired with sensible leverage, is the key to achieving meaningful returns with tolerable risk. We will make some simplifying assumptions to build intuition, derive a set of formulas with accompanying figures, and run a simple simulation to demonstrate what is required to construct and monetize a high Sharpe ratio …

Some portfolio construction heuristics Read More »

Historically, long-short equity factors have provided positive mean returns with low correlation to other assets. Most retail investors use long-only products, meaning they invest only in the long leg of the long-short factors. We will dissect factor returns into their long and short legs and further examine their performance in different states of the equity …

Dissecting factor returns in bull and bear markets Read More »

Correlations largely determine the benefits of diversification. The lower the correlation between assets, the better the diversification. It is common practice in finance to measure correlations using short-term returns. In this post, we investigate how correlations—and therefore our understanding of long-term diversification benefits—change when we measure correlations using long-term returns. Moving from monthly returns to …

Correlations for the long run Read More »

Why would anyone with a long enough time horizon invest in anything other than equities, given they have the highest expected return? The discussion has reignited following an article titled Beyond the Status Quo: A Critical Assessment of Lifecycle Investment Advice by Anarkulova, Cederburg & O’Doherty [1], in which they argue that long-term retirement savers would be …

Diversification and sensible leverage – a match made in heaven Read More »

“In the short run, the market is a voting machine but in the long run, it is a weighing machine” is attributed to Benjamin Graham. Another industry giant, John Bogle, categorized total stock market returns into two components: the fundamental return or investment return (dividend return plus earnings growth) and the speculative return (change in …

A voting machine or a weighing machine? Read More »

Unlike the realized past, the future always involves uncertainty. The uncertainty related to risk has a variety of implications that are not widely recognized. We will show analytically and demonstrate empirically and by simulations that the expected geometric return and optimal full Kelly leverage decrease as uncertainty related to risk (volatility of volatility) increases. Conversely, …

The Kelly criterion in the presence of uncertainty about risk Read More »

Academics have long debated the concept of time diversification, which questions whether time reduces the risk for stock investors or not. Prominent academics, led by Paul Samuelson, have shown (usually mathematically, employing utility functions) that time doesn’t reduce risk. However, investors and financial advisors generally believe that risk decreases with time. A good summary of …

Time diversification works (eventually) Read More »