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How to Build Your Portfolio Like a Professional Institution Investing at the institutional level involves a sophisticated blend of strategies, risk management, and performance measurement to achieve optimal returns. One of the cornerstones of creating an institutional-grade portfolio is the use of optimization methods, with particular focus on ratios such as the Sharpe Ratio, Sortino Ratio, and Omega Ratio. In this guide, we'll delve into what these ratios are, how they differ, and when to use each to construct a robust institutional-grade portfolio. Understanding the Ratios Sharpe Ratio Definition : The Sharpe Ratio, developed by Nobel laureate William F. Sharpe, measures the performance of an investment compared to a risk-free asset, after adjusting for its risk. It is calculated by subtracting the risk-free rate from the return of the portfolio and dividing by the standard deviation of the portfolio's excess returns. Usefulness : This ratio helps investors understand how much excess return they are receiving for the extra volatility that they endure for holding a riskier asset. A higher Sharpe Ratio indicates a more attractive risk-adjusted return. Sortino Ratio Definition : Similar to the Sharpe Ratio, the Sortino Ratio also measures the risk-adjusted return of an investment portfolio. However, it differs by only considering downside volatility (negative returns) rather than the total volatility of returns. Usefulness : This focus on downside risk makes the Sortino Ratio particularly useful for investors who are more concerned about potential losses than the overall volatility. A higher Sortino Ratio indicates that the portfolio is efficiently earning more on its downside risk. Omega Ratio Definition : The Omega Ratio is a more comprehensive measure that divides the returns above a certain threshold (typically the risk-free rate) by the returns below that threshold. It considers all the moments of the distribution of returns, not just the first two moments (mean and variance) like the Sharpe and Sortino ratios. Usefulness : This ratio is especially valuable for portfolios that do not follow a normal distribution of returns, providing a more holistic view of performance across different risk levels. A higher Omega Ratio indicates better performance per unit of risk. How They Differ The primary difference among these ratios lies in how they measure risk and returns: Sharpe Ratio considers the total volatility (standard deviation) of portfolio returns, treating all volatility as equal. Sortino Ratio improves on this by focusing only on downside risk, which is more relevant for investors concerned about losses. Omega Ratio goes further by considering the entire distribution of returns, offering insights into the performance across all levels of risk. Situational Use Sharpe Ratio : Ideal for general comparisons of portfolio performance where the investor is concerned with both upside and downside volatility. It's particularly useful when comparing portfolios or investments with similar risk profiles. This ratio is commonly used by most large financial institutions due to the large sums of money they manage and ensuring portfolio stability is prioritized over larger profits. Sortino Ratio : Best used when the investor's primary concern is with the downside risk rather than total volatility. This ratio is suitable for portfolios where strategies are aimed at minimizing losses rather than capturing every potential upside. This ratio is used by investors who are able to stomach more volatility in their portfolio in return for a higher probability of gains while effectively reducing equity downside. Omega Ratio : Most beneficial for analyzing portfolios with non-normal distributions of returns, such as those including options, leveraged investments, or hedge funds. It provides a nuanced view of performance across different levels of risk, making it suitable for sophisticated investment strategies that aim to manage risk in a more granular manner. Due to the nature of this ratio, only investors who have a larger risk appetite and require aggressive growth should use this ratio as the omega ratio will not necessarily be affected by high portfolio drawdowns as long as the runups are significantly higher. This means a portfolio could experience a 60% drawdown, followed by a 1000% runup, and the Omega Ratio calculation would return a high value as the probability of gains still outweigh the probability of losses. Conclusion Constructing an institutional-grade portfolio requires a nuanced understanding of both the opportunities and risks present in the investment landscape. By leveraging the Sharpe, Sortino, and Omega ratios, investors can better assess the risk-adjusted performance of their portfolios, tailoring their investment strategies to meet specific risk and return objectives. Whether you're managing a conservative fund focused on minimizing losses or a dynamic portfolio seeking to capitalize on market inefficiencies, these ratios provide critical insights that can help optimize your investment approach for superior risk-adjusted returns.

Reduce risk in portfolios without hampering returns Asset allocation is ultimately about balancing returns with risks. While it is relatively easy to reduce risk in a portfolio, it is harder to do so without diminishing its return potential. Diversification, that is, adding uncorrelated assets to the portfolio, is one of the main tools available to investors to lower such risk, but it often comes at the cost of returns. The 60/40 portfolio, a mix between 60% equities and 40% fixed income, is the bedrock of asset allocation for many investors. Adding fixed income to equities does lower volatility and improve the Sharpe ratio, in line with Markowitz’s findings in this Nobel Prize-winning work and due to the historically negative correlation between equities and investment-grade fixed income. However, it is also true that a 60/40 portfolio has tended to deliver lower returns than a 100% equity portfolio. Does it mean that investors have to choose between higher returns with increased volatility or lower returns with decreased volatility? Cliff Asness’ thought experiment: the levered 60/40 As with any problem, the solutions usually require out-of-the-box thinking. In our case, it requires to start thinking about leverage. Cliff Asness, co-founder of AQR Capital, provided such a solution in December 1996 when serving as Goldman Sachs Asset Management’s director of quantitative research with his paper ‘Why Not 100% Equities: A Diversified Portfolio Provides More Expected Return per Unit of Risk’. In his paper, Asness argues that investors can achieve competitive returns while managing risk more effectively by diversifying their portfolios with a combination of equities and bonds and using leverage. Asness designs the ‘Levered 60/40’ portfolio which leverages a 60/40 portfolio so that the volatility of the leveraged portfolio is equal to those of equities. The applied leverage is, therefore 155%. The borrowing rate used for leveraging his 60/40 portfolio is proxied by the one-month t-bill rate. In his original paper, Asness finds that, over the period 1926 to 1993, the Levered 60/40 portfolio returns 11.1% on average per year with 20% volatility. Equities, in contrast, return only 10.3% with the same volatility. For reference, the 60/40 portfolio (unleveraged) returns 8.9% with 12.9% volatility. We extended the Asness analysis to the most recent period. We observe that over this longer period, the results still hold true. The Levered 60/40 delivers higher returns than equities with similar volatility. The Sharpe ratio of the Levered 60/40 benefits from the diversification and is improved, compared to equities, with no cost to returns themselves. Leveraging the 60/40 around the world, a successful extension In Figure 2, we extend the analyses to other regions to test the robustness of such results. While the history is not as deep, Figure 2 shows similar results. Across all the tested regions, the returns and Sharpe ratio of the Levered 60/40 portfolio exceeds those of the equities alone. At the same time, the volatility is identical, and the max drawdown is reduced. Note that we do not use a 155% leverage in all those analyses; we use the relevant leverage to match the volatility of the equities in the region. Having said that, the leverage remains very similar across regions as it oscillates between 160% for global equities and 170% for Japanese equities. The theory behind the Levered 60/40 From a theoretical point of view, the idea of focusing on the most efficient portfolio possible and leveraging it to create the most suited investment for a given investor is well anchored in financial theory. When he introduced the Modern Portfolio Theory (MPT) in 1952, Harry Markowitz had already outlined the concept through the Capital Allocation Line (Markowitz, March 1952). The efficient frontier for a mix of 2 assets: US equities and US high investment-grade bonds. Note that each portfolio on the efficient frontier is the most efficient for a given level of volatility, assuming no leverage. All portfolios on the efficient frontier are not equal and have, in fact, different Sharpe ratios. Along this efficient frontier, there is a portfolio with the highest Sharpe ratio of all, called the ‘Tangential Portfolio’. This most efficient of all the efficient portfolios happens to be found where the Capital Allocation Line touches the efficient frontier. The Capital Allocation Line is the line that is tangential to the efficient frontier and crosses the Y axis (the 0% volatility axis) at a return level equal to the risk-free rate. When it comes to building the most efficient portfolio for a given level of volatility, investors have two choices. Without leverage, they can pick the portfolio with the highest return for that volatility level on the efficient frontier. If investors look for strategies with a volatility level equal to equities, equities are the most efficient portfolio. Considering potential leverage, the answer is quite different. With leverage, an investor can pick the portfolio with the relevant volatility level (in this case, the equity volatility) on the Capital Allocation Line. Portfolios on this line happen to have a Sharpe ratio equal to the Sharpe ratio of the Tangential portfolio (that is, the best Sharpe ratio of all the portfolio combinations without leverage) but with any level of volatility that may be required. We called the Leveraged Tangency Portfolio the portfolio on the Capital Allocation Line with the same volatility as the equity portfolio. This portfolio is a ‘more efficient portfolio’. The return is improved by almost 2% for the same volatility, leading the Sharpe ratio to jump from 0.27 to 0.45. Key Takeaways “Diversification is the only free lunch in Finance”, whether a real or fake H. Markowitz’s quote, epitomises the philosophy that underpins the 60/40 portfolio. It is also one of the main lessons from Markowitz's Nobel prize-winning work. Having said that, the second lesson has not been heeded as well: leveraging a good portfolio can make an even better portfolio. Overall, by leveraging a traditional 60/40 portfolio, an idea that, at WisdomTree, we call ‘Efficient Core’, investors could potentially receive a similar level of volatility present in a portfolio 100% allocated to equities but with the better Sharpe ratio of a 60/40 portfolio. Possible examples of where such Efficient Core portfolios may be used widely in multi-asset portfolios include: An equity replacement A core equity solution designed to replace existing core equity exposures. By offering return enhancement, improved risk management and diversification potential compared to a 100% equity portfolio, Efficient Core can also be used to complement existing equity exposures. A capital efficiency tool By delivering equity and bond exposure in a capital-efficient manner, Efficient Core can help free up space in the portfolio for alternatives and diversifiers. In line with the illustrations above, allocating 10% of a portfolio to this idea, investors would aim to get 9% exposure to US equities and 6% exposure to US Treasuries. This could allow investors to divest 6% from existing fixed income exposures and consider alternative assets (such as broad commodities, gold, carbon or other assets). In this scenario it could potentially be achieved without losing the diversifying benefits of their fixed income exposure. This material is prepared by WisdomTree and its affiliates and is not intended to be relied upon as a forecast, research or investment advice, and is not a recommendation, offer or solicitation to buy or sell any securities or to adopt any investment strategy. The opinions expressed are as of the date of production and may change as subsequent conditions vary. The information and opinions contained in this material are derived from proprietary and non-proprietary sources. As such, no warranty of accuracy or reliability is given and no responsibility arising in any other way for errors and omissions (including responsibility to any person by reason of negligence) is accepted by WisdomTree, nor any affiliate, nor any of their officers, employees or agents. Reliance upon information in this material is at the sole discretion of the reader. Past performance is not a reliable indicator of future performance.

The 3 Musketeers of Risk Analysis Introduction: In the world of investing, managing risk is as crucial as seeking returns. Three vital tools for assessing risk-adjusted returns are the Sharpe Ratio, Sortino Ratio, and Omega Ratio. In this post, we'll explore these ratios, their calculation, their unique features, and when to use them. 1. Sharpe Ratio: Balancing Risk and Return Measures risk-adjusted returns using total volatility (both up and down). Formula: (Return - Risk-Free Rate) / Portfolio Standard Deviation. Strength: Widely accepted and provides a simple assessment of risk-adjusted return. Weakness: Assumes normal distribution and ignores skewness. 2. Sortino Ratio: Focusing on Downside Risk Emphasizes downside risk. Formula: (Return - Risk-Free Rate) / Downside Deviation (only negative returns). Strength: Ideal for risk-averse investors and non-normally distributed returns. Weakness: Ignores upside volatility. 3. Omega Ratio: Probability of Positive Returns Evaluates risk-adjusted returns based on the probability of achieving positive returns. Formula: Probability of Positive Returns / Probability of Negative Returns. Strength: Provides insights into return probabilities and considers tail events. Weakness: Less recognized and may require more data. Conclusion: Understanding these ratios helps investors make informed decisions. The Sharpe Ratio simplifies risk-return assessment, the Sortino Ratio prioritizes downside protection, and the Omega Ratio analyzes return probabilities. Combining these ratios offers a comprehensive view of investment performance in an unpredictable financial world.

The most common malpractice in all of Trading: Back-testing Given ANY in- or out-of-sample time series, including purely random, synthetic data, anyone can generate (inflate) ANY Sharpe Ratio by repeatedly applying different trading or investment strategies to the same time series sample! By definition, purely random data has no discernible structure. Consequently, no method can exist to predict such a sequence - I.e., Sharpe Ratio = 0 must hold in all instances. Yet, ... See main graph! In the past It has been shown just how easy it is to generate Sharpe Ratios of 4, 5 or even >6, on any data, including on purely random, synthetic time series data when in fact, the only possible value in those instances should be S.R. = 0. As a matter of fact, this misleading (self-defeatists?) practice is so common and wide spread in finance and trading that the American Statistical Association considers it "unethical" (American Statistical Association ). (More importantly, it is a remarkably expensive way to fool oneself.) The above stems from applying the same rejection threshold for the null hypothesis under multiple testing will grossly underestimate the probability of obtaining a false positive. Unlike in the "other sciences", there is no "replication crisis" in finance or trading, simply because such checks don't even exist there - since those would be impossible to carry out. (Is that why the only two kinds of academic papers which never get revised or retracted are written in the fields of Finance and Theology?) The bottom line; In the common case of testing a trading or investment system, given a set of out-of-sample time series, one MUST increase the rejection threshold for the null hypothesis in proportion to the number of times ("peeks") such tests are carried out! (Good luck fooling yourself that way!) Anything less is just simple curve-fitting! For more in-depth explorations: Marcos López de Prado, Michael J. Lewis codemacher.com

How Much Gold Does Your Portfolio Need?Economists make forecasts to make weathermen look good. Trying to forecast trends in complex systems is never easy. As with weather, financial markets are influenced by a myriad of factors which can make prediction akin to gambling. Time in the market beats timing the market so a far safer bet is building a diversified and informed portfolio. As mentioned in our previous paper , gold is a crucial addition to any well-diversified portfolio. Gold offers investors the benefits of resilience during crises, diversification, and low volatility while also being a good hedge against inflation. With crisis ever-present, from pandemics and geo-political conflict to financial instability and recession, uncertainty is on everyone’s lips, including central banks which bought a record 1,135 tonnes of gold last year. Central Banks have shown no signs of slowdown going into 2023, buying 74t in Jan and 52t in Feb, the strongest start to central bank buying since 2010. It is clear why, with rising global inflation due to 2 years of unprecedented QE. A decade of cheap money has its costs which are coming back to bite both consumers and central banks. This is now being played with collapsing banks and crumbling businesses. Though governments may term these exceptions, they’re the inevitable consequence of hiking rates too fast. And even though inflation has now started to cool, it is proving stubborn and the risk of recession looms. In crisis, institutions and individuals rush to gold. It’s no wonder then that gold prices spiked in March nearing an All-Time-High above USD 2,000/oz. Gold continues to trade above the key 2000 level even in April. Even now crises show no sign of slowing. Recession talks have become commonplace and phantoms of 2008 haunt with bank collapses. The world is increasingly moving towards reshoring and friendshoring, and de-dollarization is talked about more and more. It is almost inevitable that gold will break its all-time-high soon. But, buying gold is the easy part, in fact, our previous paper covered 6 Ways to Invest in Gold. Managing gold as part of a larger portfolio is more nuanced. Allocating the right amount, finding the right entry, and knowing when to cash out are all critical. This paper aims to address two questions – 1. What are the key drivers of gold prices in this decade 2. How should investors use gold in balancing portfolios to navigate turbulent times? What Propels Gold After Its All Time High? SVB and Credit Suisse pushed it to its brink. In fact, spot prices in India, Australia, and the UK sailed even above their All-Time-High. But what propels gold now? Financial Instability Was Credit Suisse the End? “The current crisis is not yet over, and even when it is behind us, there will be repercussions from it for years to come.” - Jamie Dimon Unfortunately, Credit Suisse was likely just a symptom of the larger problem. 2-years of near-free money has inevitably led others to make risky bets which catch up to them during periods of QT. Additionally, Credit Suisse and SVB’s collapse were both set off by an unprecedentedly aggressive rate hiking cycle. Fed is stuck between a rock and a hard place as they try to control runaway inflation with aggressive rate hikes. Higher rates for longer increase the risks of financial instability. Stubborn Inflation and Recession Risks Stubborn inflation? Wasn’t inflation on its way down after almost a year? Yes and No. Although yearly inflation has definitely cooled in most countries from their peak last year, inflation continues to tick up month-by-month above the targets that central banks have set for themselves. It is not expected to reach below their targets even before 2025 in many countries. This is because although energy and commodity prices have cooled with demand waning, core inflation continues to remain stubbornly high. Additionally, food and energy prices are still volatile. On the back of this, recession risks remain high. Recently released FOMC meeting minutes showed that officials expect a recession in the second half of the year. A recession in many countries now seems inevitable. Gold shines during recession and high-inflation environments. High Interest Rates Wasn’t the Fed done hiking? Currently, CME’s FedWatch tool shows a ~72% chance of another 25bps hike next month despite the surprisingly low US CPI print. Does another 25bps matter? What’s more important is that 25bps is the peak rate and most central banks are calling this summit a pause and not a pivot. As such, rates will likely remain high for the remainder of 2023. Gold tends to perform well during high interest rate and risk-off environments. Escalating Tensions, Friendshoring, and De-Dollarization Last but definitely not least are central banks and their gold-buying binge. Though some of this can be explained by the ultra-high inflation. It is undeniably also driven by rising political tensions. The conflict in Ukraine continues to rage and the US extend its trade war against China with the CHIPS act. This is driving many of the largest economies to reshore and friendshore key supply chains. This also means relying less on the USD which can be weaponized by the US. De-dollarization has been underway for the last 23 years as the share of USD holdings in foreign exchange reserves has declined from 71.5% to 58.3% over the past 23 years. Current conditions make it more likely that the trend will accelerate. Gold inevitably benefits from all of this as it is one of the only assets that no other central bank can print or freeze. All of these factors will likely drive gold in the coming decade. But instead of setting a price target, investors can be prudent and methodical by properly allocating it as part of a larger portfolio. Using Gold in a Portfolio From 2000 until now, the following portfolios would deliver: Since 2000, gold has been the best performing asset out of the 3 main components of a basic portfolio – Large Cap stocks (SPY), Treasury Bonds (10Y), and Gold. Gold price has risen 609% compared to SPY at +193%. Investing in 10-year maturity treasury bonds would have netted investors 110% during these 23 years. As such, larger portfolio allocation towards gold would have yielded investors far more during this period. However, this comes at the downside of higher volatility. Gold has had an average 12-month rolling volatility of 15.8% over the last 23 years, slightly higher than SPY’s 14%. Still, not all volatility is bad, especially if the returns outweigh the risk. Volatility to the upside can be beneficial to investors. In order to measure the returns from the portfolio after accounting for higher volatility-associated risk, investors can measure the risk-adjusted returns using the Sharpe Ratio and Sortino Ratio. Sharpe Ratio measures the amount of excess return generated by taking on additional volatility-related risk. The higher the Sharpe Ratio, the better the portfolio is performing relative to its risk. The figure below contains the Sharpe Ratio for each of the portfolios across the last 23 years. Since each year had a different risk-free rate due to changing monetary policy, the Sharpe ratios vary for every year and there are periods during which gold-heavy portfolios have highest Sharpe ratios and others where it has the lowest. This highlights gold's sensitivity to changes in monetary policy. Sortino Ratio also measures risk-adjusted returns like the Sharpe Ratio however it only considers the risk of downside volatility. In other words, it measures return for every unit of downside risk. The figure below contains the Sortino Ratio for each of the portfolios. A key difference between the Sharpe and Sortino Ratios can be seen in the readings for 2009. Sharpe Ratio for a gold-heavy portfolio is the lowest in 2009 due to high volatility in gold prices. However, since this was volatility to the upside, the Sortino Ratio for a gold-heavy portfolio in 2009 is the highest. In 2023, a Gold heavy portfolio has performed the best and has the highest Sharpe and Sortino Ratio due to gold's relative overperformance amid the banking crisis. DISCLAIMER This case study is for educational purposes only and does not constitute investment recommendations or advice. Nor are they used to promote any specific products, or services. Trading or investment ideas cited here are for illustration only, as an integral part of a case study to demonstrate the fundamental concepts in risk management or trading under the market scenarios being discussed. Please read the FULL DISCLAIMER the link to which is provided in our profile description.

PMax Explorer Strategy (by KivancOzbilgic) - FOREX Backtesting From 4032 results we have for this strategy : * 1451 results with Profit Factor > 1 * 270 results with Profit Factor>1 and Sharpe Ratio>0 * 19 results with Profit Factor>1 and Sharpe Ratio>0 and Percent Profitable>50 * Best timeframe : 1m with 18 and 8m with 17 pairs * Best pair for all categories : OANDA:BTCUSD with 28 / BINANCE:BTCUSDT with 27 timeframes * My rating for this strategy is : 0.4712% Check my posts for all instrument categories 1st (FOREX), 2nd(CRYPTOs) and 3rd(INDICES/METALS) I will split each strategy backtesting in this manner I'm talking for strategy : PMax Explorer STRATEGY & SCREENER (by KivancOzbilgic) Oct 10, 2020 I test 29 Forex pairs from FXCM, 51 Crypto Pairs from Binance and 46 CFDs Indices and Metals from OANDA In total 126 pairs using 32 !!! timeframes 1,2,3,4,5,6,7,8,10,12,15,17,20,24,25,30,45 minutes 1,1-1/2,2,3,4,5,6,7,8,10,12,16,20 hours 1 and 2 Days In total 4032 results per strategy I like profit factor and Sharpe ratio as my main guides but also percent profitable does matter The results of forex were with 1000 contracts, default currency USD and 0.07 USD per order commission At Cryptos i use 1 contract, default currency USD and no commission because most cryptos are spread based. At Indices i use the same details as Crypto. I didn't touch any settings at the strategy for all three ideas (only the backtesting starting day where i maxed out the available data) I can't post direct links according to house rules, since i love TradingView and i play with their rules. However my profile links and my signature may help for extensive information.