# Discuss changes in risk-adjusted return (Sharpe Ratio) for individual equity markets and the equally-weighted equity portfolio

The relation between correlations and available diversificationthe changes (if any) in available diversification over time and the impact of that on global equity investing

Index Dataset: Download 20 years (last 240+1 months or the past full calendar years+1 prior month) of monthly total return or price index data for equity indices (say 4 regions of interest to you e.g., MSCI US, UK, Japan and HK); plusYTM for the US 10Y Treasury Notes (US10YTN) and a riskfree rate (US 3 Month Treasury Bill Rate).

Use total return indices if available especially if you intend to calculate some annualized compounded rates of returns. If unavailable for your chosen indices, use price indices and be aware that dividends yield is excluded from return calculations. Work out the below in Excel for every 4year period (5 snapshots for simplicity, shorter period more snapshots can be calculated):

Monthly (percentage) returns [Pt/Pt1 1]Equity indices’ correlation matrix of monthly return and period average correlation, also produce the variancecovariance matrix( σ)Annualized compounded rate of return [e.g., for 4yr, R = (Pt/Pt48)^(1/(48/12)) 1

Annualized volatility [monthly return volatility x sqrt(12)]Sharpe Ratio (SR) using the above annualized calculations and the riskfree rate [SR = (R rf)/annualized volatility]

For an equallyweighted portfolio of say 4 equity indices: annualised compounded rate of return, volatility [sqrt(𝑤′σ𝑤)] and SR. Also calculate Diversification Benefit (using 1sigma VaR) = equallyweighted volatility portfolio volatility

Correlation between MSCI US and US10YTN

Chart and compare the above metrics, including correlation pairs and their averages, to see how available diversification has changed over time and the impact on riskadjusted return (SR)

Using your above calculations and graphs, examine and discuss questions such as (but not limited to):

How did correlations (and therefore available diversification and diversification benefit) among these equity markets change over time or were they stable over this period?

Discuss changes in riskadjusted return (Sharpe Ratio) for individual equity markets and the equallyweighted equity portfolio

Think about what caused the changes (if any) in the SR of the equallyweighted equity portfolio (i.e., due to changes in individual index volatilities, correlations, returns or some combination of these factors)

Compare risk, returns and Sharpe Ratio for individual equity markets and the equallyweighted portfolio vs those of the US10YTN

How did the correlation between US Equities and US10YTN change and what is the impact (if any) on the SR of say a 60/40 US Equity/US Government Bon 