Unveiling the Influence of Investment Horizon on Portfolio Performance - A Study on Portfolio of Information Technology Stocks

Introduction

Investing in financial markets has always been driven by the pursuit of maximizing returns while managing risks. Investors employ various strategies and techniques to make informed decisions, aiming to grow their wealth over time. One crucial factor that significantly influences investment outcomes is the time horizon of the investment. The investment horizon is the duration of time an investor intends to hold an investment or a portfolio (asset) before liquidating it. It can range from days or months to years and decades. Investors have different planned investment horizons, and these variations are influenced by a wide array of factors. Some of the key factors include their financial goals, risk tolerance, age, life stage, income, and cash flow requirements. Moreover, the chosen investment strategies, personal circumstances, market conditions, transaction costs, and behavioural factors also play a vital role in shaping their investment timeframes.

Considering several factors, investors may opt for short-term strategies to capitalize on immediate gains and frequently revise their portfolios to respond to the changing market conditions and opportunities. Alternatively, they might choose a long-term approach, holding onto investments for extended periods to benefit from potential growth over time. By systematically analyzing these factors, investors can tailor their investment plans to align with their specific objectives and risk preferences. Surprisingly, the investment literature has paid little attention to the significance of the investment horizon while measuring the risk and return of a portfolio. Does the length of the investment horizon matter? If the horizon is altered, can it have notable effects on portfolio performance?

Stocks with high short-term volatility may show attractive mean returns within a short-term horizon but could exhibit different performance characteristics over a long-term horizon. Stocks that don’t see much price fluctuation in the short term might appear to have lower average returns over a very short period. However, their performance can show significant differences while considering a longer stretch of time. This discrepancy can lead to notable changes in stock performance when the investment horizon is altered. However, over longer investment horizons, the impact of underlying fundamentals and economic conditions may become more pronounced, affecting the stock’s performance differently. Hence, investors should be mindful of the investment horizon over which stock/portfolio performance is evaluated.

Research Assumptions

This study aims to address the impact of time horizon on the performance of investment with a set of assumptions:

1. Investors possess a risk-averse attitude and seek to optimize returns.
2. Investors look only at risk and return for the decision of investment horizon and all other factors are kept silent.
3. Variation in the portfolio’s performance is based on the time horizon, while keeping all other influencing factors unchanged.
4. Investors will adhere to a particular time frame for holding their stocks (no selling before or holding past the intended period).
5. Historical ex-post return distributions provide the best estimate of ex-ante returns. In other words, an investor planning to invest for one month bases decisions on means and variances calculated from past monthly returns, while an annual investor uses past annual rates.

Earlier Studies

Portfolio selection or security selection has remained a pivotal and enduring topic in modern finance, capturing the attention of scholars for decades. The inception of this field can be traced back to the pioneering contributions of Markowitz (1952) and Roy (1952). Markowitz’s groundbreaking insights emphasized the potential advantages of diversification in mitigating portfolio variance, although complete risk elimination remained elusive. Simultaneously, Roy introduced a complementary principle highlighting the trade-off between an investor’s pursuit of returns exceeding a predetermined minimum and associated risks. These foundational ideas found further extension through Merton (1969), who ventured into continuous-time scenarios, expanding the scope of portfolio selection principles. As the field evolved, researchers explored multiperiod optimization to refine portfolio strategies over extended time frames. The mathematical foundations of portfolio selection were rigorously examined by Levy (1972), who established a link between assumed investment horizons and the Reward to Variability index which was proposed by Sharpe in 1966. This connection introduced a systematic mathematical bias dependent on the chosen investment horizon.

Contributions from Li and Ng (2000), Basak and Chabakauri (2010), Czichowsky (2013), and Björk and Murgoci (2014) enriched the comprehension of multiperiod portfolio optimization. Kamara et al. (2016) explored the intricate interplay between asset risk and investment horizons. This dynamic relationship highlighted the evolving mechanisms for risk pricing across different investment time frames, fostering a deeper comprehension of risk premia and their correlation with investment horizons. Research in the field of portfolio selection has yielded significant insights into the relationship between mutual fund investment styles and varying investment horizons (Amadi and Amadi, 2019). Moreover, recent findings by Levy (2022) have emphasized a critical disparity between the extended horizons of mutual fund investors and the prevalent reliance on monthly return-based rankings, calling for a transformative shift in performance evaluation techniques.

Objectives and Hypothesis

• Objective 1: To examine the performance of a portfolio of IT stocks across different time horizons.
• Objective 2: To analyze the impact of time horizon on the performance of a portfolio of IT stocks.
• Hypothesis (H₀): Investment horizon does not influence the performance of an IT portfolio.

Data, Sample and Portfolio Weights

A portfolio consisting of seven stocks of Information Technology (IT) companies was meticulously examined, utilizing historical daily price data spanning a period of 15 years (2008 to 2022)¹. The metrics were calculated across various time horizons of 50 to 1000 trading days with an interval of 50 days, using the approach of rolling window analysis. Stocks met two criteria: (i) constituents of the Nifty IT index on the NSE, and (ii) listed prior to 2008. Weights are assigned based on market capitalization.

Table 1 – Allocation of Weights to Each Security in the Portfolio

Mathematical Methodology

The performance metrics of the portfolio were calculated using the following equations:

1. Portfolio Return (R_p)

Where R_i is the annualized return of security i, and W_i is the weight of security i.

2. Annualized Security Return (R_i)

Where h represents the time horizon in trading days, 250 represents standard trading days in a year, and r is the average return across n rolling windows: r = (∑_t=1ⁿ r_t) / n, with r_t = (P_t+h − P_t) / P_t.

3. Portfolio Risk (σ_p)

Where standard deviation is calculated as: σ = √[ ∑_t=1ⁿ (r_t − r)² / (n − 1) ].

4. Systematic Risk (β_p)

Where Nifty 50 index returns represent market returns (r_m).

5. Sharpe Ratio (SR) and Treynor Ratio (TR)

Where R_f is the risk-free rate of 6.83% based on 91, 182, and 364-day Treasury Bill yields².

6. Linear Regression Model

Where y is the dependent performance metric, h is the investment horizon in trading days, α is the intercept, β is the regression slope, and ε is the error term.

Empirical Findings

Table 2 – Performance Metrics of IT Stocks Portfolio Across Time Horizons

Linear Regression Analysis

Regression statistics assess the strength and direction of relationships between investment horizons and performance metrics:

Table 3 – Simple Linear Regression Analysis

Conclusion

This study investigated how the investment horizon affects the performance of the IT portfolio. By examining the performance metrics of the IT portfolio across various time horizons, employing a dataset spanning 15 years, the results exhibited that for a short-term, return increases with extension in time horizons, but after a certain level (350 trading days), it starts to decline as an extension in time horizon. Standard deviation rises with longer horizons, and systematic risk indicates wavy movements over different horizons. Sharpe and Treynor ratios decrease with longer horizons, signaling lower risk-adjusted returns for longer horizons. Furthermore, the systematic risk of the IT portfolio exhibits a slightly higher level of volatility when compared to the market. This suggests that the returns of the IT portfolios are likely to experience more fluctuations than the returns of the broader market.

The findings of linear regression analysis portray a regression model that fits effectively with the highly significant coefficients that allow us to reject the null hypothesis for R_p, σ_p, SR, and TR. These findings reinforce the substantial influence of the time horizon on the performance of the IT portfolio.

The study’s findings suggest that risk-averse investors should exercise caution when investing in the IT Portfolio due to its slightly elevated volatility compared to a diversified market. Additionally, careful consideration is warranted when opting for longer investment time horizons, given their association with heightened risk and lower risk-adjusted returns relative to shorter horizons. Furthermore, the study’s insights provide guidance for making informed decisions in portfolio management of customizing investment horizons within the realm of IT investments.