Experience and Foresight

About Calamos Investments

For nearly 35 years, we have helped investors like you manage and build wealth to meet their long-term individual objectives by working to capitalize on the opportunities of the evolving global marketplace. We launched our first mutual fund in 1985 and our first closed-end fund in 2002. Today, we manage five closed-end funds. Two are income-oriented total return offerings, which seek current income, with increased emphasis on capital gains potential. Three are enhanced fixed income offerings, which pursue high current income from income and capital gains. Calamos Convertible and High Income Fund (CHY) falls into this category. Please see page 5 for a more detailed overview of our closed-end offerings.

We are dedicated to helping our clients build and protect wealth. We understand when you entrust us with your assets, you also entrust us with your achievements, goals and aspirations. We believe we best honor this trust by making investment decisions guided by integrity, by discipline, and by our conscientious research.

We believe an active, risk-conscious approach is essential for wealth creation. In the 1970s, we pioneered strategies that seek to participate in equity market upside and mitigate some of the potential risks of equity market volatility. Our investment process seeks to manage risk at multiple levels and draws upon our experience investing through multiple market cycles.

We have a global perspective. We believe globalization offers tremendous opportunities for countries and companies all over the world. In our view, this creates significant opportunities for investors. In our U.S., global and international portfolios, we are seeking to capitalize on the potential growth of the global economy.

We believe there are opportunities in all markets. Our history traces back to the 1970s, a period of significant volatility and economic concerns. We have invested through multiple market cycles, each with its own challenges. Out of this experience comes our belief that the flipside of volatility is opportunity.

JOHN P. CALAMOS, SR.

CEO and Global Co-CIO

Dear Fellow Shareholder:

Welcome to your semiannual report for the six-month period ended April 30, 2013. This report includes commentary from our investment team, as well as a listing of portfolio holdings, financial statements and highlights, and detailed information about the performance and allocation of your fund. I invite you to read it carefully.

Calamos Convertible and High Income Fund (CHY) is an enhanced fixed income fund. We utilize dynamic asset allocation to pursue high current income, while also maintaining a focus on capital gains. We believe that the flexibility to invest in high yield corporate bonds and convertible securities is an important differentiator, especially given the low rates in many areas of the fixed income market.

Steady and Competitive Distributions

During the annual period, CHY provided steady monthly distributions. We believe the Fund’s distribution rate, which was 7.85%* on a market price basis as of April 30, 2013, was very competitive, given the low interest rates in many segments of the bond market.

We understand that many closed-end fund investors seek steady, predictable distributions instead of distributions that fluctuate. Therefore, this Fund has a level rate distribution policy. As part of this policy, we aim to keep distributions consistent from month to month, and at a level that we believe can be sustained over the long term. In setting the Fund’s distribution rate, the investment management team and the Fund’s Board of Directors consider the interest rate, market and economic environment. We also factor in our assessment of individual securities and asset classes. (For additional information on our level rate distribution policy, please see “The Calamos Closed-End Funds: An Overview” on page 5 and “Level Rate Distribution Policy” on page 35.)

Market Environment

Today’s market conditions remind me of the often tumultuous 1970s, when macro events fueled uncertainty and volatility. This time around, however, massive accommodative

monetary policy from the Federal Reserve and central banks around the world has supported the global equity markets and their overall recoveries. However, this aggressive easing policy has also driven government bond yields in developed markets to historic lows. As a result, the search for income continued to be a primary concern for many investors, contributing to distortions in the equity markets as well.

The U.S. stuck to its slow-growth trajectory, adding to its growing string of consecutive quarters of economic expansion. A recovering housing market and rising equity markets contributed to a “wealth effect” that carried through to retail and auto sales. Although sequestration cast a shadow at the end of the year that carried into 2013, the country managed to avoid the fiscal cliff, and the passage of a new continuing resolution has prevented a Washington shutdown.

Elsewhere, we continued to see underwhelming euro zone GDP and ongoing tensions between the haves and have-nots. Italy’s ill-fated election, as well as Cyprus’ woes and the EU’s missteps in addressing them, underscored the tensions in the EU and the complexities of the bailout-austerity cycle. There was better news coming out of Japan, however, as the Bank of Japan took steps during the period to reverse deflation, resulting in better factory output, consumer confidence and business sentiment for that key global economy.

Conditions were best in the U.S., as economic recovery continued at a slow and steady pace. U.S. stocks rallied to a double-digit performance, with the S&P 500 Index¹ returning an impressive 14.42% for the six-month period. Global markets also participated in the upswing, as the MSCI World Index², a measure of developed market equity performance, posted a robust 13.78% gain. Meanwhile, emerging markets lagged their developed market counterparts for the period amid concerns of slowing growth and less accommodative monetary policy in several key economies, but the MSCI Emerging Markets Index³ still managed a gain of 5.40%.

Many of the Calamos funds utilize convertible securities, and this area of the market also enjoyed the six-month rally, as the BofA Merrill Lynch All U.S. Convertible Ex-Mandatory Index⁴ returned 12.69%, prompted by lower-quality higher yielding securities. High yield issuance continued to maintain a steady pace, while performance for the six-month period was also healthy, with a 7.21% return in the Credit Suisse High Yield Index⁵. The lower yielding U.S. bond market was more muted, however, as the Barclays Capital U.S. Aggregate Bond Index⁶ posted a gain of just 0.90%.

Global Outlook: Cautious Optimism

Our global outlook remains cautiously optimistic, and we believe, now more than ever, that active management and diversification are crucial to long-term investing success.

We expect the global economic recovery to continue at a measured pace, led by the U.S. and the emerging markets. Our greatest concerns relate to euro zone GDP and a potential slowdown in earnings growth, globally. We believe that valuations and long-term secular trends (including those related to the EM consumer)

support our positioning. Recent housing and consumer data in the U.S. has been encouraging, and although some of China’s first quarter economic data (GDP and industrial production) has fallen short of estimates, numbers remain high in absolute terms and relative to developed markets.

On the back of central bank intervention and investors’ quest for income, valuations for areas such as staples have become stretched to a point that we believe merits caution. Meanwhile, we believe that the valuations of growth equities are attractive by many measures. For example, U.S. growth equities are highly compelling on the basis of free cash flow yields versus 10-year Treasury yields, as well as on a P/E basis versus value stocks. Many growth-rich but dividend-poor technology stocks are especially undervalued. After strong performance in the first half of 2012, we’ve seen the sector give some back, but the fundamentals still look attractive from both top-down and bottom-up perspectives.

We are also encouraged by trends in the U.S. and global convertible markets. Economic growth has supported increased issuance globally, and we continue to find attractively valued convertibles that offer the characteristics we seek—that is, a balance between equity participation and potential downside resilience.

Our Use of Leverage*

We have the flexibility to utilize leverage in this Fund. Over the long term, we believe that the judicious use of leverage provides us with opportunities to enhance total return and support the Fund’s distribution rate. Leverage strategies typically entail borrowing at short-term interest rates and investing the proceeds at higher rates of return. During the reporting period, we believed the prudent use of leverage would be advantageous given the economic environment, specifically the low borrowing costs we were able to secure. Overall, our use of leverage contributed favorably to the returns of the Fund, as the performance of the Fund’s holdings exceeded the costs of our borrowing activities.

Consistent with our focus on risk management, we have employed techniques to hedge against a rise in interest rates. We have used interest rate swaps to manage the borrowing costs associated with our leverage activities. Interest rate swaps allow us to “lock down” an interest rate we believe to be attractive. Although rates are at historically low levels across much of the fixed income market, history has taught us that rates can rise quickly, in some cases, in a matter of months. We believe that the Fund’s use of interest rate swaps is beneficial because it provides a degree of protection should a rise in rates occur.

A Global, Long-Term Perspective

Despite our broadly constructive outlook for equities and the global economy, we expect continued choppiness in the markets, and would not be surprised to see the equity market correct off recent highs, with

overpriced sectors potentially coming under particular pressure. We believe this can create new buying opportunities, and we are carefully assessing opportunities across industries.

In this environment, we believe that maintaining long-term focus, global perspective and a commitment to diversified asset allocation are vital to investing success. We recognize that our role is to understand and adapt to the markets we are in, and we believe that our experience, proprietary research and active approach position us well in this regard. We continue to enhance our team and our approach, adding new resources, including a dedicated value investing team, additional specialized team members and more risk management capabilities.

If you would like any additional information about this Fund or our other closed-end offerings, please contact your financial advisor or our client services team at 800.582.6959 (Monday through Friday from 8:00 a.m. to 6:00 p.m., Central Time), or visit us at www.calamos.com. We thank you for your continued trust.

Sincerely,

John P. Calamos, Sr.

CEO and Global Co-CIO,

Calamos Advisors LLC

Before investing, carefully consider a fund’s investment objectives, risks, charges and expenses. Please see the prospectus containing this and other information or call 800.582.6959. Please read the prospectus carefully. Performance data represents past performance, which is no guarantee of future results. Current performance may be lower or higher than the performance quoted.

Unmanaged index returns assume reinvestment of any and all distributions and, unlike fund returns, do not reflect fees, expenses or sales charges. Investors cannot invest directly in an index.

Investments in overseas markets pose special risks, including currency fluctuation and political risks. These risks are generally intensified for investments in emerging markets. Countries, regions, and sectors mentioned are presented to illustrate countries, regions, and sectors in which a fund may invest. Fund holdings are subject to change daily. The Funds are actively managed.

The information contained herein is based on internal research derived from various sources and does not purport to be statements of all material facts relating to the securities mentioned. The information contained herein, while not guaranteed as to the accuracy or completeness, has been obtained from sources we believe to be reliable. There are certain risks involved with investing in convertible securities in addition to market risk, such as call risk, dividend risk, liquidity risk and default risk, that should be carefully considered prior to investing. This information is being provided for informational purposes only and should not be considered investment advice or an offer to buy or sell any security in the portfolio.

This report is for informational purposes only and should not be considered investment advice.

CONVERTIBLE AND HIGH INCOME FUND

INVESTMENT TEAM DISCUSSION

The Fund’s Investment Team discusses strategy, performance and positioning for the six-month period ended April 30, 2013.

Q.  To provide a context for its performance, please discuss the Fund’s strategy and role within an asset allocation.

A.  Calamos Convertible and High Income Fund (CHY) is an enhanced fixed income offering, seeking total return through a combination of capital appreciation and current income. It provides an alternative to funds investing exclusively in investment-grade fixed income instruments, and seeks to be less sensitive to interest rates. Like all five Calamos closed-end funds, the Fund seeks to provide a steady stream of distributions paid out on a monthly basis and invests in multiple asset classes.

We invest in a diversified portfolio of convertible securities and high yield securities. The allocation to each asset class is dynamic and reflects our view of the economic landscape as well as the potential of individual securities. By combining these asset classes, we believe that we are well positioned to generate capital gains as well as income. We believe this broader range of security types also provides us with increased opportunities to manage the risk and reward characteristics of the portfolio over full market cycles.

We seek companies with respectable balance sheets, reliable debt servicing, and good prospects for sustainable growth. While we invest primarily in securities of U.S. issuers, we favor those companies that are actively participating in globalization with geographically diversified revenue streams and global business strategies.

Q.  How did the Fund perform over the reporting period?

A.  The Fund gained 8.29% on a net asset value (NAV) basis and 8.84% on a market price basis for the six-month period ended April 30, 2013, versus the 7.21% return of the Credit Suisse High Yield Index for the same period.

Q.  How do NAV and market price return differ?

A.  Closed-end funds trade on exchanges, where the price of shares may be driven by factors other than the value of the underlying securities. The price of a share in the market is called market value. Market price may be influenced by factors unrelated to the performance of the fund’s holdings. A fund’s NAV return measures the return of the individual securities in the portfolio, less fund expenses. It also measures how a manager was able to capitalize on market opportunities. Because we believe closed-end funds are best utilized as a long-term holding within asset allocations, we believe that NAV return is the better measure of a fund’s performance.

SINCE INCEPTION MARKET PRICE AND NAV HISTORY THROUGH 4/30/13

Performance data quoted represents past performance, which is no guarantee of future results. Current performance may be lower or higher than the performance quoted. The principal value of an investment will fluctuate so that your shares, when sold, may be worth more or less than their original cost. Returns at NAV reflect the deduction the Fund’s management fee, debt leverage costs and other expenses. You can obtain performance data current to the most recent month end by visiting www.calamos.com.

Q.  Please discuss the Fund’s distributions during the annual period.

A. We employ a level rate distribution policy within this Fund with the goal of providing shareholders with a consistent distribution stream. The Fund provided a steady distribution stream over the period. Monthly distributions were $0.0850 per share. The Fund’s annual distribution rate was 7.85% of market price as of April 30, 2013.

We believe that both the Fund’s distribution rate and level remained attractive and competitive, as low interest rates limited yield opportunities in much of the marketplace. For example, as of April 30, 2013, the dividend yield of S&P 500 Index stocks averaged 2.08%. Yields also remained low within the U.S. government bond market, with 10-year U.S. Treasurys and 30-year U.S. Treasurys yielding 1.70% and 2.88%, respectively.

Q.  The Fund is currently trading at a discount to its NAV. Please discuss this discount.

A.  As of the close of the reporting period, the Fund was trading at a discount of 4.49%. This means that its market share price is 4.49% less than its NAV price. At the beginning of the reporting period, the Fund was trading at a discount of 4.97%. As we have noted in the past, we believe that this may be favorable for long-term investors seeking to purchase shares because investors can buy shares of the portfolio at a price that is lower than the fair value of the portfolio, as measured by its NAV.

Q.  What factors influenced performance over the reporting period?

A.  During the period, high yield bonds performed strongly as credit spreads tightened in the space by 108 basis points, as measured by J.P. Morgan. As spreads narrowed due to demand for income coupled with an improving equity market, yields on high yield bonds fell to historic lows. Lower credit qualities in the high yield space were outperformers as investors demand for yield inspired interest in the CCC-rated tier. However, given our more conservative approach to managing the high yield space, the Fund did not participate in the gains that exposure to these types of securities would have provided.

Consistent with their demand for yield, investors gravitated towards more defensive, higher dividend paying stocks as they invested in the equity markets. Although the Fund’s convertible exposure participated measurably in the improving stock markets, its gravitation towards less equity- or credit-sensitive names reduced returns relative to the general convertible market index.

Fund asset allocations are based on total investments and may vary over time.

Specifically, security selection in the financials sector, especially asset managers, sparked performance. The Fund’s selection in consumer discretionary was also beneficial, with holdings in the catalog retail industry adding to returns. Security selection in information technology hindered performance, in spite of the fact that the Fund’s overweight in the space was additive. Security selection in materials, especially the Fund’s commodity-related holdings, held back returns, as gold mining names lagged.

Q.  How is the Fund positioned?

A.  We have emphasized mid-grade corporate credits in the Fund as we believe they offer compelling yields and capital appreciation potential at levels of risk that we believe are appropriate. In the current environment, we have also been selective in regard to the most speculative issues, reflecting our concerns that these credits may not presently provide adequate compensation for associated risk. We continue to maintain a higher average credit quality in our high yield securities relative to the Credit Suisse High Yield index.

We have slightly decreased the Fund’s positions in the consumer discretionary, energy and information technology sectors, although in the latter two areas the Fund continues to be overweight relative to the index. We have measurably increased the Fund’s position in the financials sector, which we believe may benefit from improvements in the economy, especially the housing market. We have also increased exposure to industrials, and the Fund is now overweight in that sector relative to the index. We have slightly reduced the Fund’s exposure to health care, but it continues to be overweight to the sector.

We have continued to emphasize convertible securities that offer asymmetric risk-return characteristics versus the underlying stocks. We have been encouraged by the fact that this segment of the market has benefited from strong performance. We continue to see attractive opportunities in growth equities, and believe that convertibles offer an attractive way to gain exposure to this area while providing yield to satisfy investors’ demand for income.

Q.  What is your outlook for the Fund?

A.  As we look forward, our global economic outlook remains one of cautious optimism. We believe the U.S. appears positioned to continue on its slow and steady recovery. Improvements in the housing sector and rising equity markets have contributed to consumer confidence, which appears to by buoying the economy. Job growth also seems to be improving, albeit slowly. Many high yield issuers look well positioned for the future, having taken advantage of low rates to lower borrowing costs. We continue to favor mid-grade corporate credits. We also favor moderate duration bonds, as history has shown that interest rate increases can move quickly. Given current spread levels, we expect performance of high income strategies to reflect bottom-up fundamental considerations, rather than a further narrowing of spreads.

We are encouraged by trends in the U.S. and global convertible markets. Economic growth has supported increased issuance globally, and we see this as positive for the Fund. We continue to find attractively valued convertibles that offer the characteristics we seek by striking a balance between equity participation and a potential downside protection. Although we are constructive on equities and the global economy, we see persistent choppiness in the market—an environment that we believe underscores the benefits of access to convertibles as an investment strategy.